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10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is imposed, (b) 2 particular women must not sit together, (c) each woman is to be between 2 men?

10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is imposed, (b) 2 particular women must not sit together, (c) each woman is to be between 2 men?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is imposed, (b) 2 particular women must not sit together, (c) each woman is to be between 2 men? 11. In how many ways can 10 objects be split into two groups containing 4 and 6 objects respectively? 12. In how many ways can a committee of 5 people be chosen out of 9 13. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee? 14. From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning. 15. Find the number of (a) combinations and (b) permutations of 4 letters each that can be made from people? the letters of the word Tennessee.
Transcribed Image Text:10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is imposed, (b) 2 particular women must not sit together, (c) each woman is to be between 2 men? 11. In how many ways can 10 objects be split into two groups containing 4 and 6 objects respectively? 12. In how many ways can a committee of 5 people be chosen out of 9 13. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee? 14. From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning. 15. Find the number of (a) combinations and (b) permutations of 4 letters each that can be made from people? the letters of the word Tennessee.
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