Combinations From One Set

Combinations From One Set

Combination Formula

is the number of combinations of

“n” different objects that can be formed by taking

“r” of them at a time (r ≤ n)

!

( )! !n r

nC

n r r

Combinations From One Set

Example 1: How many different sets of 3 golf

clubs could be selected from a bag containing 11

different clubs to be used in a tournament such as

was described in the introduction to this section?

Solution: A set of 3 golf clubs is needed and there are

11 from which to choose. The order in which the clubs

are selected is not important because any 3 clubs will

form only one set no matter what order they are

selected.11 3

11!165

(11 3)!3!C different possible sets

Combinations From One Set

Example 2: In Lotto 649 participants are to

choose any 6 integers from the set of integers

{1, 2, 3, …, 49}. How many tickets would one have

to buy in order to guarantee a win?

Solution: To purchase a ticket one needs to

select a set of 6 digits from 49 digits. Thus there are:

49 6

49!

(49 6)!6!

13983816

C

different ticket combinations

Homework

Do #1 – 11 odd numbers only on pages 208 and 209 from Section 6.5 for Wednesday June 3rd