A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously.

Answers

Answer 1

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

[tex]\mathbf{n = 5}[/tex] --- the number of digits

[tex]\mathbf{r = 3}[/tex] ---- the number of actions

Each of the three actions can either be:

Pressing one buttonPressing a pair of buttons

The number of ways of pressing a button is:

[tex]\mathbf{n_1 = ^5C_1}[/tex]

Apply combination formula

[tex]\mathbf{n_1 = \frac{5!}{(5-1)!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5!}{4!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}[/tex]

[tex]\mathbf{n_1 = 5}[/tex]

The number of ways of pressing a pair is:

[tex]\mathbf{n_2 = ^5C_2}[/tex]

Apply combination formula

[tex]\mathbf{n_2 = \frac{5!}{(5-2)!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5!}{3!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}[/tex]

[tex]\mathbf{n_2 = 10}[/tex]

So, the number of ways of performing one action is:

[tex]\mathbf{n =n_1 + n_2}[/tex]

[tex]\mathbf{n =5 + 10}[/tex]

[tex]\mathbf{n =15}[/tex]

For the three actions, the number of ways is:

[tex]\mathbf{Action = n^3}[/tex]

[tex]\mathbf{Action = 15^3}[/tex]

[tex]\mathbf{Action = 3375}[/tex]

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

https://brainly.com/question/4546043


Related Questions

Find m Give explanation please

Answers

Answer:

m < FGN = 88°

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).

Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:

The following equality statement can be established according to the exterior angle theorem:

m < E  + m < F  = m <FGN

38 + 6x - 10 = 7x + 18

Combine like terms:

28 + 6x = 7x + 18

Subtract 6x from both sides:

28 + 6x - 6x = 7x - 6x + 18

28 = x + 18

Subtract 18 from both sides:

28 - 18 = x + 18 - 18

10 = x

Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.

m < E  + m < F  = m <FGN

38° + (6x - 10)° = (7x + 18)°

38 + 6(10) - 10 = 7(10) + 18

38 + 60 - 10 = 70 + 18

88 = 88 (True statement).

Therefore, m < FGN = 88°

each month for 6 months laras bank account balance decreased by $84. Witch quantity describes the total change in laras bank account balance

Answers

Answer:

Step-by-step explanation:

0

Ig1000+log342 - 1 -123​

Answers

Answer:

log(342) - 121

Step-by-step explanation:

-121 + log(342) is a transcendental number

-115.165189262937394847783249972808918485...

the sum of a number and 11

Answers

Hello!

The sum of a number and 11:

Let's say that the number is x. So the expression "the sum of a number and x" looks like this:

x+11

Hope this helps you!

~Just an emotional teen who listens to her favourite songs

[tex]SilentNature[/tex]

Hey there!

Guide:

• The word “sum” means “add” or “addition”

• The word “difference” means “subtract” or “subtraction”

• The word “product” means “multiply” or “multiplication”

• The word “quotient” means “divide” or “division”

NOW THAT WE HAVE ALL OF THAT INFORMATION, WE CAN SOLVE FOR YOUR EQUATION

“The SUM of a number and 11”

Well since the “number” is unknown we can label it as “a” so we can know what we’re ADDing to 11…

So, your equation should be: a + 11

Answer: a + 11

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Suppose y varies directly as x, and y=14 when x=4. What is the value of y when x=9

Answers

Given :-

y varies directly as x, and y=14 when x=4.

To Find :-

the value of y when x=9 .

Solution :-

According to Question ,

y = kx ( k is constant )

When y = 14 and x = 4 ,

14 = k(4)k = 14/4k = 7/2

When x = 9 ,

y = 7/2*9 y = 63/2y = 31.5

May I please receive help?
Please

Answers

Answer:

<R=56 degrees; <Q=62 degrees; <S=62 degrees

Step-by-step explanation:

5x+12=4x+22 (This is because the two angles are congruent to each other.)

x+12=22

x=10

Now, plug it in.

5(10)+12=50+12=62 degrees

62(2)=124 degrees (This is because the two angles are congruent and equal)

180-124=56 degrees


What is 0.000000000325 in scientific notation?

Answers

Answer:

3.25*10^-10(is.3.25E−10)

3.25x10^-9

The coefficient must be between  1 and 10The negative exponent means the number is small

Hope it helps!

~Just a joyful teen

[tex]GraceRosalia :)[/tex]

Find the slope of each line.

Answers

Answer:

Slope: - 5/2

Step-by-step explanation:

Order each set of numbers from least to greatest.
1: -4,-7, 3, 16,-18
2: -12, 20, 24, -39, -24
3: 9,-57,-64, -32, 0
4: -3,-13, -24,-1,-8

Answers

Answer:

1. -18,-7,-4,3,16

2. -39,-24,-12,20,24

3. -64,-57,-32,0,9

4. -24,-14,-8,-3,-1

Step-by-step explanation:

Negative numbers are always least.

Hello I really need help 30 points

Answers

Answer:

C

Step-by-step explanation:

The vertical line test determines that more than 1 point falls on the vertical line making the graph NOT a function

subtract (3x^3-2x+5)-(-4x^3+3x-6)

Answers

Answer:

7x^3-5x+11

Step-by-step explanation:

(3x^3-2x+5)-(-4x^3+3x-6)

Distribute

3x^3-2x+5+4x^3-3x+6

Simplify

7x^3-5x+11

3x³-2x+5-(-4x³+3x-6)3x³-2x+5+4x³-3x+63x³+4x³-2x-3x+5+67x³-5x+11

The perimeter of this rectangle si __________ units

Answers

The answer for this question is 14

L + B (x2) = 7+2 (x2)

9 x 2 = 18 (si units can be cm, m..?)

Find an equation in point-slope form for the line having the slope m= - 4 and containing the point (4,5).
The equation in point-slope form is
(Use integers or fractions for any numbers in the equation.)

Answers

Answer:   y - 5 =  - 4 (x - 4)

Step-by-step explanation:

The point-slope form of a line is (y - y₁) = m(x - x₁)

Since we know the slope (m) is -4

And the point  ( x₁, y₁ ) is (4, 5)

Then we can just plug these into the equation above:

                               ⇒  y - 5 =  - 4 (x - 4)

I often use Desmos to check my answer. As seen below, the equation does pass through the point (4, 5).                                      

32.28 in
expanded form​

Answers

Step-by-step explanation:

expanded form is adding each place value together with zeros replacing all other spots

32.28

30.00 + 2.00 + 00.20 + 00.08

3. Due to leakage, 30% of the water was lost from a water tank. If
only 340 liters of water is left in the tank now, find the total
capacity of the water tank?
HELPP

Answers

Answer:

1133.3 liters of water after leakage.

Step-by-step explanation:

x*.30=340

x=340/.30

x=1133.33

The total capacity of the water tank is 1133.33 liters of water after leakage.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have given Due to leakage, 30% of the water was lost from a water tank. If only 340 liters of water is left in the tank now, then we need to find the total capacity of the water tank.

x*.30 = 340

x = 340/.30

x = 1133.33

Hence, the total capacity of the water tank is 1133.33

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

The car travels with constant acceleration reaching a speed of v m/s after 6 seconds. The car then travels at a constant speed of v m/s for a further 2 seconds. The car travels a total distance of 150 metres. Work out the value of v

Answers

v=30m/s velocity is 30 ms-1

I am a 4 digit number.My hundred's digit is 4 less than my thousands digit.My unit's digit is 7 less than my ten's digit.My ten's digit is 3 more than my hundred's digit.My thousand's digit is the largest single digit number.what number am i?​

Answers

Answer:

9581

Step-by-step explanation:

RIGHT


ACUTE


OBTUSE


EQUIANGULAR

Answers

Step-by-step explanation:

option B is correct answer ( Acute angle triangle)

hope this helps you.

Answer:

Acute triangle

Step-by-step explanation:

Acute triangle have less than 90 degrees

Directions:Classify the following polynomials by degree and number of terms.

ANYONE PLEASE HELP ME WITH MY QUESTIONS 2 AND 3 I REALLY NEED THE ANSWER RIGHT NOW BECAUSE I HAVE TO PASS THIS LATER I HOPE Y’ALL CAN HELP ME:(
I’LL MARK BRAINLIEST FOR THOSE WHO CAN ANSWER IT CORRECTLY!

Answers

Answer:

Question 2: The degree is 3 and the terms are 2, Binomial

Question 3: The degree is 2 and the terms are 3, Polynomial

Step-by-step explanation:

Please help! See algebra question..

Answers

Answer:

n=-10

Step-by-step explanation:

n+3=-7

n=-7-3

n=-10

this helps thank you

branlist please

Answer:

n = -10

Step-by-step explanation:

solving a one step equation with a missing variable

step 1: subtract 3 from both sides of the equation then simplify

ex: n + 3 - 3 = -7 - 3   (n = -10)

step 2: take your answer of n which is -10 and add plug it in into your original equation n + 3 = -7 and solve to check your answer

ex: n + 3 = -7   (-10 + 3 = -7)

add

-10 + 3 = -7

-7 = -7   (if both sides of the equation are the same numbers like -7 = -7 then your answer is true making n = -10 your answer) i would love to get brain if this is correct and helps <(^w^)>

PLEASE HELP IM BEGGGINGGG

Answers

Answer:

the answer is (a) a//b

Step-by-step explanation:

perpendicular means that two lines that do not cross over each other.

Here’s another one.. so sorry if this confused you..

(Also I got this question wrong..)

Answers

Answer:

hmmm did you try 14?

It’s prob 13,


I dunno.. I keep thinking since it has the eighth meaning 8. Do 20-8=13

Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)

Answers

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

Step by step :

x² = 12² + 10²

x² = 144 + 100

x² = 244

x = 2[tex]\bold{\sqrt{61}}[/tex]cm

Can anyone help asap please

Answers

Step-by-step explanation:

a=32(alternate angles are equal)

b=a=32

c=17(all sides of rhombus are equal in length)

d=17(all sides of rhombus are equal in length)

e=90

f=90(diagonals intersect at right angles)

Solve. Show work

Y = -1/2 (-2) + 2

Answers

Answer:

[tex]→y = \frac{ - 1}{2} ( - 2) + 2[/tex]

[tex]→y = 1 + 2[/tex]

[tex]→y = 3[/tex]

Answer:

[tex]y=3[/tex]

Step-by-step explanation:

First distribute:

[tex]y=-\frac{1}{2} (-2)+2[/tex]

[tex]y=1+2[/tex]

Add:

[tex]y=3[/tex]

Hope this helps! :)

Find the measure of each angle indicated 12,13,14

Answers

Answer:

Step-by-step explanation:

12. 15 (3x5x1)

13.  8  (4x2x1)

14. 18 (6x3x1)

hello can anyone help with this?

The distance between Heysham and the Isle of Man is 80 km.
A hovercraft travels at 50 km per hour.
How long does the journey take?

Answers

50/1 =80/x
50x=80
Divide both sides of the equal sign by 50 to get variable by itself
x= 1.6
Your answer is 1.6 of an hour for the journey

Answer:

1 hour 36 minutes

Step-by-step explanation:

Amount of time the journey takes = 80km ÷ 50km/h

                                                        = 1.6h

                                                        = 1h 36mins

Look at the image and determine a answer please.

Answers

Answer:

Dividing

Step-by-step explanation:

z = -72

(re-asking this question) please help asap! ill give brainliest.
write 571/7 as a mixed number

(the numerator is 7, while 571 is the denominator)

Answers

Answer:

Using a calculator, if you typed in 517 divided by 7, you'd get 73.8571. You could also express 517/7 as a mixed fraction: 73 6/7.

Step-by-step explanation:

so 73 6/7 is your answer

Answer:

81 4/7

Step-by-step explanation:

Does this help?

A walking path across a park is represented by the equation y=-2x-7. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,-3). Identify the equation that represents the new path.

A. y = 1/2 x - 2

B. y = 2x +1

C. y = -2x-7

D. y = -1/2 x- 4

Answers

Answer:

d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

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