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  • A group of 8 people, including 3 men and 5 women, is to be seated in a row of 8 chairs. In how many different ways can the 3 men be seated together?Opt

A group of 8 people, including 3 men and 5 women, is to be seated in a row of 8 chairs. In how many different ways can the 3 men be seated together?

Option: 1

24000


Option: 2

36000


Option: 3

49000


Option: 4

81000


Answers (1)

best_answer

Given that,

There are 8 people who must be seated in a row on 8 chairs.

Therefore, if we find the number of ways in which all 3 men occupy consecutive seats and subtract this number from the total number of ways in which the 8 people can be arranged among themselves, we will get the required answer.

The 8 people can be arranged among themselves in {}^8 P _5 ways

Thus,

{}^8 P _5=40320

Assume that the 3 men are one entity. The total number of ways in which they can be arranged among themselves is 3! Ways.

Also, the set of 3 men and the other people can be arranged among themselves in 6! ways.

Thus, the total number of ways in which 3 men are together is given by,

3! \times 6!=6 \times 720\\ 3! \times 6!=4320

Thus, the number of ways in which all 3 men will not occupy consecutive seats is given by,

40320-4320=36000

Therefore, the total number of ways to arrange the people is 36000.

Posted by

Gautam harsolia

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