Q. 275.0( 2 Votes )

# 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

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