Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Twenty two people purchase raffle tickets. Three winning tickets are selected at random if the first prize is $\$1000$ , the second prize is $\$500$ , and the third prize is $\$100$ , in how many different ways can the prizes be awarded? $\newline$ There are $\square$ different ways in which the prizes can be awarded (Simplify your answer).

View step-by-step help

View step-by-step help

Identify independent and dependent variables

Full solution

Q. Twenty two people purchase raffle tickets. Three winning tickets are selected at random if the first prize is

\$1000

, the second prize is

\$500

, and the third prize is

\$100

, in how many different ways can the prizes be awarded?

\newline

There are

\square

different ways in which the prizes can be awarded (Simplify your answer).

Identify the problem: Identify the problem. $\newline$ We need to determine the number of different ways to award three distinct prizes among $22$ people.
Determine the approach: Determine the approach. $\newline$ Since the prizes are distinct, we can use permutations to calculate the number of ways to award the prizes. The formula for permutations is $P(n, r) = \frac{n!}{(n - r)!}$ , where $n$ is the total number of items, and $r$ is the number of items to choose.
Calculate first prize: Calculate the number of ways to award the first prize. $\newline$ There are $22$ people and only one first prize, so there are $22$ ways to award the first prize.
Calculate second prize: Calculate the number of ways to award the second prize. $\newline$ After awarding the first prize, there are $21$ people left. So, there are $21$ ways to award the second prize.
Calculate third prize: Calculate the number of ways to award the third prize. $\newline$ After awarding the first and second prizes, there are $20$ people left. So, there are $20$ ways to award the third prize.
Calculate total ways: Calculate the total number of different ways to award the three prizes. $\newline$ To find the total number of ways to award the three prizes, we multiply the number of ways to award each prize together: $22 \times 21 \times 20$ .
Perform calculation: Perform the calculation. $22 \times 21 \times 20 = 9,240$ .
Conclude solution: Conclude the solution. $\newline$ There are $9,240$ different ways in which the prizes can be awarded.

More problems from Identify independent and dependent variables

Question

This equation shows how the distance traveled by a car is related to the time spent driving.

d = 50t + 10

t

represents the time in hours, and the variable

d

represents the distance in miles. How far does the car travel in

2

Posted 3 months ago

Question

The equation shows how the cost of buying pencils is related to the number of pencils purchased.

\newline

c= 0.5p+2

\newline

p

represents the number of pencils, and the variable

c

represents the total cost. How much does it cost to buy

10

Posted 3 months ago

Question

This equation shows how the total score in a game is related to the number of points scored per level.

s = 100l + 250

l

represents the levels completed, and the variable

s

represents the total score. What is the total score after completing

3

Posted 1 month ago

Question

The equation shows how the amount of paint needed is related to the area to be painted.

p = 2a + 5

a

represents the area in square meters, and the variable

p

represents the amount of paint in liters. How much paint is needed for an area of

8

Posted 1 month ago

Question

This equation shows how the total bill for a meal is related to the number of people sharing the meal.

\newline

b = 15n + 35

\newline

n

represents the number of people, and the variable

b

represents the total bill. What is the total bill for a meal shared by

4

Posted 3 months ago

Question

Poppy the dog weighs

p

pounds, and Yumi the cat weighs

y

pounds. If Poppy weighs

36

more pounds than Yumi does, which of the following equations correctly describes the relationship between their weights?

\newline

1

\newline

p+y=36

\newline

p+36=y

\newline

p-y=36

\newline

y-p=36

Posted 1 month ago

Question

Calvin and Melvin are two of Santa's elves. The number of toys they build is given by

11 c+8 m

c

is the number of candy canes Calvin eats for breakfast and

m

is the number of candy canes Melvin eats for breakfast. How many toys do they build when Calvin eats

5

candy canes and Melvin eats

3

candy canes for breakfast?

Posted 1 month ago

Question

2 w+4

\newline

Carly is cutting a piece of paper stock based on the width of a photo. The expression above describes the length of the paper stock, in inches, for a photo that is

w

inches wide. If the photo is

8

5

inches wide, what is the length of the paper stock in inches?

Posted 27 days ago

Question

Calvin and Melvin are two of Santa's elves. The number of toys they build is given by

11 c+8 m

c

is the number of candy canes Calvin eats for breakfast and

m

is the number of candy canes Melvin eats for breakfast.

\newline

How many toys do they build when Calvin eats

5

candy canes and Melvin eats

3

candy canes for breakfast?

\newline

Posted 2 months ago

Question

The approval rating of a certain politician is changing at a rate of

r(t)

percent of the population per month (where

t

is the time in months).

\newline

\int_{0}^{3} r(t) d t

\newline

1

\newline

(A) The rate of change of the approval rating of the politician when

t=3

\newline

(B) The average rate of change of the approval rating during the first three months

\newline

(C) The change in the percent of the population who approves of the politician during the first three months

\newline

(D) The percent of the population who approves of the politician when

t=3

Posted 1 month ago