In how many ways can 3 boys and 3 girls sit in a row

Solution:

Given, 3 boys and 3 girls sit in a row.

We have to find the ways in which 3 boys and 3 girls can sit in a row.

Permutations of n different objects taken r at a time is, the total number of ways in which n objects can be arranged at r places in a line and is given by

ⁿPr = n! / (n - r)!

Total number of boys and girls, n = 3 + 3 = 6

So, ⁶P₆ = 6! / (6 - 6)!

= 6! / (0!)

We know, 0! = 1

So, ⁶P₆ = 6!

= 6 × 5 × 4 × 3 × 2 × 1

= 30 × 24

= 720

Therefore, 3 boys and 3 girls can sit in a row in 720 ways.

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In how many ways can 3 boys and 3 girls sit in a row

Summary:

3 boys and 3 girls sit in a row in 720 ways.