WARM-UP By yourselves, make a list of 4 things that you would bring on a desert island. Imagine that you could only bring 3 of the 4 things on your list.

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Presentation transcript:

WARM-UP By yourselves, make a list of 4 things that you would bring on a desert island. Imagine that you could only bring 3 of the 4 things on your list. How many ways can you choose 3 things from the list

DISCUSSIOIN In doing the warm-up, what was most important when selecting the items that you would bring with you to a desert island? Was order important at all?

Combinations

SUBSET A set A is a subset of set B, if every element of A is an element of B “Everything that is in the set A, is also in the set B Ex: The set {a,b,c} is a subset of the set {a,b,c,d,e}

PERMUTATIONS vs. COMBINATIONS Permutations We are concerned with the order of the objects P(n,k) Combinations We do NOT care about the order of the objects; we ONLY care about the objects that are chosen C(n,k)

DISCUSSION Explain why a “combination” lock should really be called a “permutation” lock.

PRACTICE 1)C(7,1) 2)C(6,0) 3)P(10,5)/5! 4)C(6,0) 5)C(m,m)

WORD PROBLEM? How many 5-card poker hands are possible with a 52-card deck?

WORD PROBLEM? We want to find the total number of subsets of 5 cards we can choose from 52 cards; so order is NOT important

WORD PROBLEM? C(52,5)=52!/5!(47)!

MORE PRACTICE!!! ty/e/combinations_1 ty/e/combinations_1 ty/e/permutations_1 ty/e/permutations_1