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?

# 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?

1. A
34,000
2. B
35,000
3. C
36,000
4. D
37,000

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### 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,

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

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

Hence, the correct option is 3.

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