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Section 11.2 Permutations and Combinations

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Section 11.2 Permutations and Combinations

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    1. Section 11.2 Permutations and Combinations

    2. Factorial n! = n×(n-1)×(n-2)×…×3×2×1 Permutations A permutation is an arrangement of objects in a certain order. Permutation Formula for Distinct Objects

    3. Example: A university Volleyball team consists of 6 players whose position are ranked 1 through 6. If a coach has 10 players from which to choose, how many different teams can the coach select?

    4. Example: The Kentucky Derby had 16 horses entered in the race. How many different finished of first, second, third, and fourth place were possible?

    5. Applying Several Counting Techniques Example: Five women and 4 men are to be seated in a row of 9 chairs. How many different seating arrangements are possible if (a) there are no restrictions on the seating. (b) the women sit together and the men sit together

    6. Permutations of identical objects The number of distinguishable permutations of n objects of r different types, where k1 identical objects are of one type, k2 of another, and so on, is given by

    7. Example How many distinct ways can the letters of the word MISSISSIPPI be arranged? INDIANA SET ANA OHIO ILLINOIS

    8. Example: If 7 identical dice are rolled, find the number of ways two 4’s, one 5, and four 6’s can appear on the upward faces.

    9. Combinations A combination is a collection of objects for which the order is not important. Combination Formula: C(n,k)=P(n,k) / k! Example: A basketball team consists of 12 players. In how many different ways can a coach choose the five starting players, order is not considered?

    10. Example: A committee of five is chosen from 7 math majors and 6 economic majors. How many different committees are possible if the committee must include 2 math majors and 3 economic majors.

    11. Counting Problems with Cards From a standard deck of playing cards(52 cards), five are chosen. How many five-card combinations contain Five hearts? Five cards of the same suit 4 kings 3 kings and 2 Aces

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