1) Joleen is on a shopping spree. She buys six tops, three shorts and 4 pairs of

Question

1) Joleen is on a shopping spree. She buys six tops, three shorts and 4 pairs of sandals. How many different outfits consisting of a top, shorts and sandals can she create from her new purchases? If she knows which shorts to put on, how many different ways does she still have? 2) We have bought 10 things to give as Christmas gifts. In how many ways can we separate 5 for the family and 5 for friends? (order does not matter) 3) We have bought 10 things to give as Christmas gifts. In how many ways can we give 4 of them as presents to 4 different friends (and keep 6 for others)? (order matters) 4) Having the letters: A, B, C, D, E, F, O, U, in how many different ways we can form words of 6 letters (which may have no meaning) in a way, that we always alternate consonants and vowels? (all letters following a CVCVCV or VCVCVC patterns, where V and C stand for vocal and consonants – so we choose 3 vocals and consonants out of 4).

Explanation / Answer

1. This can be done in 6*3*4 ways or 72 ways. If she knows which shorts to wear, the other two things can be put in 6*4=24 ways

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