MATH 122 AND MATH 130
PERMUTATIONS AND COMBINATIONS I
1. A building has five entrances. In what number of ways can one enter the building and leave by a different entrance?
2. With the letters of the word CHOSEN, how many four-letter words can be formed that end in a vowel?
3. If each of nine boys is to receive a book, how many different distributions can be made with four identical algebra books and five identical geometry books?
4. How many distinct signals can be made with six flags displayed in vertical order all at one time, if three are yellow, two are blue, and one is red?
5. How many different committees of four can be chosen in a club having thirty-two members?
6. In how many different orders can four French, three English, and three German books be arranged on a shelf so that all the books in each language are together?
7. A white die and a black die are rolled. a) In what number of ways can the dice show their points? b) How many of these show a total of seven points?
8. If the digits 1, 2, 3, 4, 5, 6, and 7 are used without repetitions, a) how many numbers each of five figures can be formed? b) How many end in 25?
9. a) How many different committees of five can be selected from 12 persons? b) If a certain person is to be included? c) If a certain person is to be excluded?
10. From five black balls and six white balls, how many selections of five balls can be made so that a) exactly two are black? b) at least two are black?
11. a) What number of different quartets can be selected from six boys and five girls? b) How many of these quartets consist of two boys and two girls?
12. How many numbers between 20,000 and 40,000 can be made with the five digits 1, 2, 3, 4, and 5 without repeating any digit?
1. = 20 2. = 120 3. = 126
4. = 60 5. = 35960 6. 3!4!3!3! = 5184
7. a) = 36 b)
8. a) = 2520 b) = 60
9. a) = 792 b) = 330 c) = 462
10. a) 2 black: = 200 b) 3 black: = 150; 4 black: = 30;
5 black: 1 way Total = 381
11. a) = 330 b) = 150 12. = 48