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8. Permutations
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Q2 of 140 Page 317

There are 5 men and 5 ladies to dine at a round table. In how many ways can they sit so that no ladies are together?

Let first arranged 5 men in the round table by 4! (by using the formula (n-1)! Mention above)

Now there are 5 gaps created between 5 men (check the figure)



So we arrange 5 ladies in this gap by 5!


A total number of ways to arrange 5 men and 5 ladies is 5! × 4! = 2880


More from this chapter

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7

There are 4 candidates for the post of a chairman, and one is to be elected by votes of 5 men. In how many ways can the vote be given?

1

In how many ways can 6 persons be arranged in

(i) a line, (ii) a circle?


3

In how many ways can 11 members of a committee sit at a round table so that the secretary and the joint secretary are always the neighbours of the president?

4

In how many ways can 8 persons be seated at a round table so that all shall not have the same neighbours in any two arrangement?

Questions · 140
8. Permutations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1 1 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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