Unit 7 Combinatorics 7 3 Combinations Combinations u

Unit 7 Combinatorics 7. 3 Combinations

Combinations u Mathematically, we are dealing with combinations whenever… – all selections come from a single group of items – no item may be selected more than once – the order of arrangement does not matter (i. e. : ABCD is considered the same as DCBA 2

Definition u. A combination is an ordering of distinct objects in a “straight line” without any regard to the order of the items. We say that we are forming a combination of n objects taken r at a time. u The number of n objects taken r at a time is denoted by C(n, r) or n. Cr. 3

The Combinations Formula u If we make r selections from a group of n items, the number of combinations (arrangements in which order does not matter) is u Again – – n is the total number of choices r is the number of places to fill 4

Practice u If a committee of 3 people is needed out of 8 possible candidates and there is not any distinction between committee members, how many possible committees would there be? u Suppose that you select 3 different flavors of ice cream in a shop that carries 12 flavors. How many flavor combinations are possible? u How many different five-card poker hands can be dealt from a standard deck of 52 cards? 5

Counting and Technology u u u u Using the graphing calculator Type the number you have to chose from (total in set – this is n) Math button and over to PRB (probability) #2: n. Pr #3: n. Cr Type the number you are choosing from the set (this is r) Hit enter and total possibilities are displayed on your home screen 6