In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
Given: Number of boys = 6 and number of girls = 5
To find: Possible number of arrangements in a group photograph
Let boys be b1, b2, b3, b4, b5, b6 and girls be g1, g2, g3, g4, g5
Possible arrangements are
b1 b2 b3 b5 b6 b4
g2 g4 g1 g5 g3
b2 b1 b5 b3 b4 b6
g2 g4 g5 g1 g3
In this arrangement, we are arranging boys and girls separately
Formula used:
Number of arrangements of n things taken all at a point = P(n, n)
∴ Number of ways to arrange boys
= the number of arrangements of 6 things taken all at a time
= P(6, 6)
{∵ 0! = 1}
= 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 720
Formula used:
Number of arrangements of n things taken all at a point = P(n, n)
∴ Number of ways to arrange girls
= the number of arrangements of 5 things taken all at a time
= P(5, 5)
{∵ 0! = 1}
= 5!
= 5 × 4 × 3 × 2 × 1
= 120
Now, we will get total number of ways by multiplying their separate arrangements
∴ Total number of ways
= 720 × 120
= 86400
Hence, possible number of arrangements in which 6 boys and 5 girls can be arranged for a group photograph with provided conditions are 86400