Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve by the method of your choice. Twenty-two people purchase raflle tickets. Three winning tickets are selected at random. If first prize is $1000, second price is $500, and third prize is $100, in how many different ways can the prizes be awarded? There are different ways in which the prizes can be awarded. (Simplify your answer.)

Solve by the method of your choice.\newlineTwenty-two people purchase raflle tickets. Three winning tickets are selected at random. If first prize is $1000 \$ 1000 , second price is $500 \$ 500 , and third prize is $100 \$ 100 , in how many different ways can the prizes be awarded?\newlineThere are different ways in which the prizes can be awarded.\newline(Simplify your answer.)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Understanding integersright chevron icon

Full solution

Q. Solve by the method of your choice.\newlineTwenty-two people purchase raflle tickets. Three winning tickets are selected at random. If first prize is $1000 \$ 1000 , second price is $500 \$ 500 , and third prize is $100 \$ 100 , in how many different ways can the prizes be awarded?\newlineThere are different ways in which the prizes can be awarded.\newline(Simplify your answer.)
  1. Determine Number of Ways: We need to determine the number of ways to award three distinct prizes to three people out of 2222. This is a permutation problem because the order in which the prizes are awarded matters (first, second, and third are distinct).
  2. Select First Prize Winner: First, we select a winner for the first prize. There are 2222 possible people who could win this prize.
  3. Select Second Prize Winner: After awarding the first prize, we have 2121 remaining people who could win the second prize.
  4. Select Third Prize Winner: Finally, after awarding the second prize, we have 2020 remaining people who could win the third prize.
  5. Calculate Total Number of Ways: To find the total number of ways the three prizes can be awarded, we multiply the number of choices for each prize together: 2222 choices for the first prize, 2121 choices for the second prize, and 2020 choices for the third prize.
  6. Perform Multiplication: The calculation is 22×21×2022 \times 21 \times 20.
  7. Final Result: Performing the multiplication gives us 22×21×20=924022 \times 21 \times 20 = 9240.
  8. Final Result: Performing the multiplication gives us 22×21×20=924022 \times 21 \times 20 = 9240.Therefore, there are 92409240 different ways the three prizes can be awarded.

More problems from Understanding integers

Question
Function g g can be thought of as a scaled version of f(x)=∣x∣ f(x)=|x| .\newlineWhat is the equation for g(x) g(x) ?\newlineChoose 11 answer:\newline(A) g(x)=−43∣x∣ g(x)=-\frac{4}{3}|x| \newline(B) g(x)=43∣x∣ g(x)=\frac{4}{3}|x| \newline(C) g(x)=−34∣x∣ g(x)=-\frac{3}{4}|x| \newline(D) g(x)=34∣x∣ g(x)=\frac{3}{4}|x|
Get tutor helpright-arrow

Posted 2 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 53 \frac{5}{3} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=−53∣x∣ y=-\frac{5}{3}|x| \newline(B) y=35∣x∣ y=\frac{3}{5}|x| \newline(C) y=−∣x−5∣+3 y=-|x-5|+3 \newline(D) y=∣x−3∣+5 y=|x-3|+5
Get tutor helpright-arrow

Posted 4 months ago

Question
Aiden has $200 \$ 200 with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get 4040 hats. If Aiden purchases only t t -shirts, he will get 80 80 t\mathrm{t} -shirts. Which of the following best models the relationship between the number of hats, h h , and the number of t \mathrm{t} -shirts, t t , that Aiden could purchase with this money?\newlineChoose 11 answer:\newline(A) 40h+80t=400 40 h+80 t=400 \newline(B) 80h+40t=200 80 h+40 t=200 \newline(C) 5h+2.5t=200 5 h+2.5 t=200 \newline(D) 2.5h+5t=200 2.5 h+5 t=200
Get tutor helpright-arrow

Posted 4 months ago

Question
We want to find the intersection points of the graphs given by the following system of equations:\newline{x−y=−4y=5(x+1)2−3 \left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right. \newlineOne of the intersection points is (−2,2) (-2,2) .\newlineFind the other intersection point. Your answer must be exact.
Get tutor helpright-arrow

Posted 4 months ago

Question
Derrick has 22 \mathbf{2 2} dollars. Colleen has x x dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?\newlineChoose 11 answer:\newline(A) x−22 x-22 \newline(B) x+22 x+22 \newline(C) 22x 22 x \newline(D) 22x+22 22 x+22
Get tutor helpright-arrow

Posted 4 months ago

Question
Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 3030 meters and a depth of 1515 meters. He wants to increase the radius to 4040 meters and the depth to 2020 meters. How much more water will the pond hold, in thousands of cubic meters?\newline(Round to the nearest thousand cubic meters.)
Get tutor helpright-arrow

Posted 25 days ago

Question
Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are 3636 inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?\newlineChoose 11 answer:\newline(A) 3232 inches\newline(B) 4242 inches\newline(C) 5555 inches\newline(D) 6060 inches
Get tutor helpright-arrow

Posted 18 days ago

Question
Ari thinks the perfect milkshake has 55 scoops of ice cream for every 33 spoonfuls of caramel. Freeze Zone makes batches of milkshakes with 1010 scoops of ice cream and 77 spoonfuls of caramel.\newlineWhat will Ari think about the amount of caramel in Freeze Zone's milkshakes?\newlineChoose 11 answer:\newline(A) Freeze Zone's milkshakes have too much caramel.\newline(B) Freeze Zone's milkshakes have too little caramel.\newline(C) Freeze Zone's milkshakes are just right.
Get tutor helpright-arrow

Posted 2 months ago

Question
Nayeli lights a 4 m2 4 \mathrm{~m}^{2} space with 1212 candles. Citlali lights a 10 m2 10 \mathrm{~m}^{2} space with 3030 of the same type of candles.\newlineWhose space is lit brighter?\newlineChoose 11 answer:\newline(A) Nayeli's area\newline(B) Citlali's area\newline(C) The spaces are equally bright.
Get tutor helpright-arrow

Posted 4 months ago

Question
Lashawn makes scrambled eggs with 33 spoonfuls of salsa for every 22 eggs. Gilberta adds 77 spoonfuls of salsa for every 55 eggs.\newlineWhose scrambled eggs have a stronger salsa taste?\newlineChoose 11 answer:\newline(A) Lashawn's eggs\newline(B) Gilberta's eggs\newline(C) The dishes of scrambled eggs have equal salsa tastes.
Get tutor helpright-arrow

Posted 2 months ago

View all (20)