Question

In how many ways can 10 boys and 10girls sit in a row so that no two boys sit together?

Answer 1

Answer:

one girl and one boy on 1seat

Answer 2

In (10!*10!) ways 10 boys and 10 girls sit in a row so that no two boys sit together.

Given:

There are 10 boys and 10 girls.

To Find:

We have to find that in how many ways can 10 boys and 10 girls sit in a row so that no two boys sit together.

Solution:

This is a simple problem for permutation and combination.

Let us tackle this question.

we can easily solve this question as follows.

We have to arrange seats for girls and boys alike, one girl after one boy, then one girl after one boy and so on.

So, We can permute 10 seats for girls in 10! ways.

Again we can permute 10 seats for boys in 10! ways.

Therefore,

With the condition that no two boys sit together,

10 girls and 10 boys can sit in a row in (10! * 10!) ways.

i.e., 10 girls and 10 boys can sit in a row in (3628800*3628800)ways.

Hence, in (10!*10!) ways 10 boys and 10 girls sit in a row so that no two boys sit together.

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