Question

Joe has one book each for algebra, geometry, history, psychology, Spanish, English and Physics in his locker. How many different sets of three books could he choose?

Answer 1

There are 35 different sets of 3 books Joe could choose

Explanation:

* Lets explain how to solve the problem

- Combination is a collection of the objects where the order doesn't

matter

- The formula for the number of possible combinations of r objects from

a set of n objects is nCr = n!/r!(n-r)!

- n! = n(n - 1)(n - 2)................. × 1

Lets solve the problem

- Joe has one book each for algebra, geometry, history, psychology,

Spanish, English and Physics in his locker

∴ He has seven books in the locker

- He wants to chose three of them

∵ The order is not important when he chose the books

∴ We will use the combination nCr to find how many different sets

of three books he can choose

- The total number of books is 7

∴ n = 7

∵ He chooses 3 of them

∴ r = 3

∵ 7C3 = 7!/3!(7 - 3)! = 7!/3!(4!)

∴
`7C3=((7)(6)(5)(4)(3)(2)(1))/([(3)(2)(1)][(4)(3)(2)(1)])=35`

∴ 7C3 = 35

* There are 35 different sets of 3 books Joe could choose