# mt4 - x x-1(1 x 26 3 How many integers between 1000 and...

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Homework 4, Math 245, Fall 2010 Due Wednesday, October 20 in class. The solution of each exercise should be at most one page long. If you can, try to write your solutions in LaTex. Each question is worth 2 points. 1. A club of 8 men and 10 women has to select a committee of 4 people with at least one man and one woman. In how many ways can this be done ? If among the four committee members, one is the chairperson, one is convener, one is secretary and one is treasurer, in how many ways can the four members of the committee be chosen ? 2. What is the coeﬃcient of x 20 in the binomial expansion of ( 2 x 3 - 3 x ) 8 ? What is the coeﬃcient of x 12 in (1 +
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Unformatted text preview: x + x-1 )(1 + x ) 26 ? 3. How many integers between 1000 and 9999 have distinct digits ? How many of these numbers are even ? How many of these numbers are odd ? 4. There are 16 books on a shelf. In how many ways can you choose 5 books such that the selection does not include any two neighboring books ? 5. How many words can be made from the letters of the word FLEECE ? 6. Bonus Question! You roll n identical dice. Show that there are exactly ( n +5 5 ) distinct outcomes. (For example, when n = 1, there are ( 1+5 5 ) = ( 6 5 ) = 6 outcomes. When n = 2, there are ( 2+5 5 ) = ( 7 5 ) = 21 outcomes)....
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