Question

THERE ARE 6 BOOKS ON A READING LIST. STUDENTS MUST READ ANY 3 OF THE BOOKS ON THE LIST. IN HOW MANY WAYS CAN A STUDENT SELECT ANY 3 BOOKS?

Answer 1

To solve this problem, you must use the Combination Formula:

Cr(n,r)=n! /r!(n-r)!

n: The number of things it can be chosen (n=6).
r: The number of things you choose (r=3).
!: The symbol of The Factorial Function, which means that descending numbers are multiplied.

In Combinations the order of the objects does not matter, so we have:

Cr(n,r)=n!/r!(n-r)!
C(6,3)=6!/3!(6-3)!
C(6,3)=6!/3!
C(6,3)= 6x5x4x3!/3x2x1x3!
C(6,3)=6x5x4/3x2x1
C(6,3)=120/6
C(6,3)=20

In how many ways can a student select any 3 books?
The answer is: In 20 different ways.