A combination is a sample (group, set, committee, collection) of items drawn from a sample space where order doesn't distinguish one sample of things from another sample of the same things. For example, a poker hand formed by drawingcards 8H, 3C, KD, QS, and 2D is the same hand formed by drawing QS, 3C, KD, 8H,and 2D.

Suppose the sample space contains things a, b, and c, and two things are drawn without replacement. The possible samples produced are ab, ac, and bc.There are three possible combinations.

A problem where you should not try toenumerate the possible combinations. What if you want to determine how many committees of 4 can be formed from 7 people. There are =PERMUT(7,4) = 840 permutations possible sequences of 4 people formed from 7. For each combination of 4 has 4 x 3 x 2 x 1 = 4! permutations. So, there are 840 permutations (4! permutations/combination) = 35 committees of size 4 that can be formed from 7. Better screen some of the candidates first to reduce the sample space.

In general, the number of combinations = PERMUT(N, n) n!,or doing it all with one Excel function, it's=COMBIN(N,n).

• Example: How many 5-card hands can be drawn from a 52 card deck?There are 2,598,960 possible hands. compute it?

How many committees of 3 people can be formed from 7 people?