Combinations and Permutations

Question 1

If 15 people are competing for 3 different prizes, how many ways could the prizes be awarded?

Accepted Answer

15P3

Question 2

A 5 person committee is selected from a class of 30 students. How many possible committees?

Accepted Answer

30C5

Question 3

How many ways can the gold, silver, and bronze medals be awarded in a race with 10 people?

Accepted Answer

10P3

Question 4

You have 10 friends and can take any number of them to the beach, how many ways can you do it?

Accepted Answer

210

Question 5

I have 10 different fruit, and I'm going to use 3 to make a smoothie. How many ways?

Accepted Answer

10C3

Question 6

How many ways can you distribute 20 people into two rooms labeled A and B?

Accepted Answer

220

Question 7

There are 7 different toppings available and you can get as many as you want. How many pizzas?

Accepted Answer

27

Question 8

12 people are in a room and everyone shakes everyone else's hand exactly once; how many shakes?

Accepted Answer

12C2

Question 9

How many binary strings of length 8 contain exactly three 1's and five 0's?

Accepted Answer

8C3

Question 10

How many ways could you rearrange the letters LMNOP?

Accepted Answer

5!

Question 11

How many different binary strings (sequences of 1's and 0's) of length 8 are there?

Accepted Answer

28

Question 12

How many ways can 10 people be split into two teams: The Banana Slugs and The Weasels.

Accepted Answer

10C5

Question 13

How many ways can a president, VP, and secretary be chosen from a class of 25 students?

Accepted Answer

25P3

Questions 13