# Math Help - Probability

1. ## Probability

Solvbe this:-

There are six boys and girls who sits in one row. Find the probability that no two boy sits together.

2. Six boys can be placed in 7 places in 7 C 1 ways.

Probability of no 2 boys sitting together is 2/7.

please correct me if I am wrong.

Thanks,
Ashish

3. ## Probability

Hello vivek_master146
Originally Posted by vivek_master146
Solvbe this:-

There are six boys and girls who sits in one row. Find the probability that no two boy sits together.
Do you mean six boys and six girls? It is vital that you write down questions like this exactly as they were first written!

If there are six boys and six girls, then we can arrange them in a row in 12! ways.

If no two boys sit together, then either:

• the boys sit in places 1, 3, ..., 11 (and the girls in places 2, 4, ..., 12); or

• the boys sit in places 2, 4, ..., 12 (and the girls in places 1, 3, ..., 11)

Each of these arrangements can be done in 6! x 6! different ways. So the probability that one of these occurs is

$\frac{2\times 6!\times 6!}{12!}= \frac{1}{462}$