Set Theory and Combinatorics How many ways are there to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, u appear consecutively and the last letter in the ordering is not a vowel? (Hint: Every vowel appears to the left of a consonant.)

In three-card poker, a hand consists of three cards dealt from a deck of 52. How many different three-card poker hands are possible? (Order is not important.)

A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?

Choosing Outfits A girl has five skirts, eight blouses, and 12 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear?Assume that each item matches all the others, so she is willing to wear any combination.