Discrete Math Section 15.3 Solve problems using permutations and combinations Read page 578 www.youtube.com/watch?v=6J_wY6N_l7s    Combinations and permutations are used to select a smaller set (subset) from a larger set of elements. Permutations are used when the order of the elements is important. Combinations are used when the order of the elements is not important.

Permutations Combinations nCr = n!___ (n – r)! r! nPr = n!___ (n – r)! Used to choose r items out of a set of n items Combinations nCr = n!___ (n – r)! r! Used to choose r items out of a set of n items

For a certain raffle, 845 tickets are sold. a. In how many ways can four $50 gift certificates be awarded? b. In how many ways can a $100, a $50, a $20, and a $10 gift certificate be awarded? a. 845C4 = 845 ! 845−4 ! = b. 845P4 = 845 ! 845−4 ! 4! = 2.10924768 x 1010 5.062194431 x 1011

A calculator used to evaluate permutations and combinations TI 84 evaluate 7P3 type “7” MATH PRB nPr Type “3” ENTER TI Nspire Scratch pad Calculate Menu Probability Permutations nPr(7,3)

In how many ways can a hand of five cards be dealt from a 52 card deck? Order does not matter…. 52C5 = 2,598,960

The science club has 24 members The science club has 24 members. A president, secretary, and treasurer are to be elected. In how many ways can the three officers be elected? Order is important… 24P3 = 12144

Assignment Page 580 Problems 2,3,4,6,8,10,15,17,20