STAT1301 (Assig1)

# STAT1301 (Assig1) - 09/10 THE UNIVERSITY OF HONG KONG...

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09/10 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE Assignment 1 Due Date: September 23, 2009 (Hand in your solutions for Questions 5, 12, 14, 20, 26, 28, 30, 37) 1. A total of 8 different gifts are to be distributed among 12 children. How many distinct results are possible if no child is to receive more than one gift? 2. From a group of 9 women and 5 men a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together; (b) 2 of the women refuse to serve together; (c) 1 man and 1 woman refuse to serve together? 3. In how many ways can 10 people be seated in a row if (a) there are no restrictions on the seating arrangement; (b) persons A and B must sit next to each other; (c) there are 6 men and 6 women and no 2 men or 2 women can sit next to each other; (d) there are 6 men and they must sit next to each other; (e) there are 5 married couples and each couple must sit together? 4. Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if (a) a student can receive any number of awards; (b) each student can receive at most 1 award? 5. ( Poker ) If it is assumed that all poker hands are equally likely, what is the probability of being dealt 5 52 (a) one pair? (This occurs when the cards have denominations a, a, b, c, d where a, b, c, and d are all distinct.) (b) two pairs? (This occurs when the cards have denominations a, a, b, b, c , where a, b, and c are all distinct.) (c) three of a kind? (This occurs when the cards have denominations a, a, a, b, c .) (d) a straight? (Five consecutive cards of any suits which are not all the same, including 10, J, Q, K, A .) (e) a flush? (Five cards of the same suit and not all in consecutive order.) (f) full house? (This occurs when the cards have denominations a, a, a, b, b .) (g) four of a kind? (This occurs when the cards have denominations a, a, a, a, b .) (h) a straight-flush? (Five consecutive cards of the same suit, including 10, J, Q, K, A .) 6. From a group of 5 lawyers, 7 accountants, and 9 doctors, a committee of three is selected at random. What is the probability that the committee has more lawyers than doctors? P. 1

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09/10 7. We have 30 thousand dollars that must be invested among 4 possible opportunities. Each investment must be integral in units of 1 thousand dollars, and there are minimal investments that need to be made if one is to invest in these opportunities. The minimal investments are 3, 3, 4, and 5 thousand dollars. How many different investment strategies are available if (a) an investment must be made in each opportunity; (b) investments must be made in at least 3 of the 4 opportunities? 8.
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STAT1301 (Assig1) - 09/10 THE UNIVERSITY OF HONG KONG...

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