Question

There are 4 boys and 4 girls. In how many ways can they sit in a row?

Answer 1

Consider 4 boys and 4 girls as 8 different persons / individuals. There, we will find the number of ways in which 8 different people can sit in a row.

Complete step by step solution: Suppose there are 8 person and they have totally 8 seats in a row as follows:

Now, we take one person (from a group of 4 boys and 4 girls). That one person can sit in any of the 8 seats. Now, there are 7 seats left.
Now, we similarly take another person from leftover ones (total now sever person). That person can take his seats in any of the 7 places.
Now there are 6 seats left & 6 people to be seated.
We go the same way.We choose one person from remaining 6 and that person can sit in any of the 6 places left.
Continuing this way, the last person will have only one seat left that he had to sit.
Total no of ways 8 person (4 boys & 4 girls) sit in a row is
$8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$
$=8$ !
$=40,320$
Total no of ways in which 4 boys and 4 girls can sit in a row is $8!$ which is 40,320 ways.

Note: Alternate method: There is an alternate method by which we can directly solve the question. There is a direct formula which says:
The number of ways in which n different persons can be seated in row is n!. Here, n=8. So, we can directly put n in the formula to get the answer which is 8!.