Sorry. Maths question.

Question

I have fifteen books in total. If five of them are written by me, and I pick four random books to take on holiday, what is the probability that exactly 2 of my books are written by me?

Answer 1

There are 5 books written by you, and you want to pick 2 of them.

 

There are 10 books NOT written by you, and you want to pick 2 of them also, since you want to pick 4 books total.

 

So the total number of ways you can pick two books written by you and two books not written by you is:

 

₅C₂ * ₁₀C₂ = 5!/3!2! * 10!/8!2! = 10 * 45

 

The total number of ways to pick 4 books out of 15 is ₁₅C₄ = 15!/11!4! = 1365

 

So the probability of picking exactly 2 books written by you is 45 / 1365 = 0.033 = 3.3%