4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either be N or B? 5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sit together? 6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seats of (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats. 7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and that they must be first, second and third, respectively. How many different batting orders are there for the team? 8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sit together and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members of the group and want to sit together all the time? 9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular persons want to sit next to each other? 10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in a string (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?
4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either be N or B? 5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sit together? 6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seats of (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats. 7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and that they must be first, second and third, respectively. How many different batting orders are there for the team? 8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sit together and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members of the group and want to sit together all the time? 9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular persons want to sit next to each other? 10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in a string (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 54SE: How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and...
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Transcribed Image Text:4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either
be N or B?
5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sit
together?
6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seats
of (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats.
7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and that
they must be first, second and third, respectively. How many different batting orders are there for the team?
8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sit
together and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members of
the group and want to sit together all the time?
9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular persons
want to sit next to each other?
10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in a
string (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?
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