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A six person committee composed of Alan, Bob, Connie, Dolph, Edward, and Francis

ID: 3201607 • Letter: A

Question

A six person committee composed of Alan, Bob, Connie, Dolph, Edward, and Francisco is to select a chairperson, secretary, and treasurer. How many selections are there in which Dolph is an officer and Francisco is not an officer? A committee composed of Morgan, Tyler, Mac, and Leslie is to select a president and a secretary. How many selections are there in which Tyler is president or not an officer? Consider a set of 5 distinct computer science books, 3 distinct mathematics books, and 2 distinct art books. In how many ways can these books be arranged on a shelf if all five computer science books are on the left and both art books are on the right?

Explanation / Answer

Let the people be denoted as A B C D E and F respectively.

It is known that F does not take any position and D definitely takes a position, so we have 4 people left for 2 positions.

The first position has 4 options, and second position has the left 3 option.

So the number of ways= 4*3= 12