Permutations and Combinations

Question 1

In how many ways can 6 friends line up for a photo where Jill stands between Mark and Paul?

Accepted Answer

2(4!)

Question 2

In how many ways can 5 friends (A, B,C, D, E) sit in a row where B and C sit together?

Accepted Answer

2(4!)

Question 3

In how many ways can you order 4 red cars and 7 blues cars so the red cars are all together?

Accepted Answer

(8!)(4!)

Question 4

What is the probability a random selection of 3 letters contains the letter H in HYPERBOLA ?

Accepted Answer

8C2 / 9C3

Question 5

I have 5 Rock CDs and 3 Pop CDs. How many ways can I select 5 CDs where 3 are Rock?

Accepted Answer

(5C3)(3C2)

Question 6

5 people are chosen on a bowling team from 10. A won't play if B plays. How many ways?

Accepted Answer

196

Question 7

In how many ways can 9 girls and 3 boys be ordered so no boy is next to another boy?

Accepted Answer

(720)(9!)

Question 8

3 Maths, 4 English, 2 French books: How many arrangements so Maths and English books together?

Accepted Answer

3456

Question 9

In how many ways can a committee of 2 men and 2 women be selected from 6 men and 4 women?

Accepted Answer

(6C2)(4C2)

Question 10

In how many ways can I arrange the letters in MATHEMATICS ?

Accepted Answer

(11!) / (2!)(2!)(2!)

Questions 10