Combinations

Combinations

In class on Monday we continued Unit 5 with Combinations. Recall that a permutation is an ordered collection of elements. The formula is given by:
nPr = n! / (n-r)!

A combination is an unordered collection of elements.

Notation: C(n, r) or nCr

Formula: nCr = n! / r!(n-r)!


With a permutation, we select and order the elements (two actions). With a combination we only select the elements (one action). Must use the formula for a combination – can not use the dash method.

Example 1: Evaluate:

a) 10C2

n=10 r=2

10C2 = 10! / 2! (10-2)!
= 10! / 2! 8!
= 45

b) 8C3
n=8 r=3

8C3 = 8! / 3! (8-3)!
= 8! /3! 5!
= 56


Example: A student has a penny, a nickel, a dime, a quarter, and a half dollar and wishes to leave a tip consisting of exactly 3 coins. How many different tips are possible?

n=5 r=3

5C3 = 5! / 3! (5-3)!
= 5! / 3! 2!
= 10