Five boys and three girls are sitting in a row of eight seats. In how many ways can they be seated so that not all the girls sit side by side?

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34,000

35,000

36,000

37,000

answer is C.

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Detailed Solution

Given that,
Total no. of boys is 5.
Total no. of girls is 3.
No. of persons to be seated in a row is 8.
First, we have to calculate the number of ways so that the person can be seated without any restriction is,

= 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320

Then, the number of arrangements in which all girls sit together is,

= P 3 3 × P 5 5 × P 6 1 = 3! × 5! × 6 = 6 × 120 × 6 = 36 × 120 = 4320

The total number of ways in which all three girls not sit together is,

= 40320 − 4320 = 36000

Hence, the correct option is 3.

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