In how many ways can $6$ boys and $5$ girls be arranged for group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

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Solution

Five girls can sit on chairs in a row in $^{5} P_{5} = 5!$ ways.

Also, $6$ boys can stand behind them in a row in $^{6} P_{6} = 6!$ ways.

Hence the total number of ways $= 5! \times 6! = 120 \times 720 = 86400$

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In how many ways can 6 boys and 5 girls be arranged for group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

Five girls can sit on chairs in a row in 5P5=5! ways.Also, 6 boys can stand behind them in a row in 6P6=6! ways.Hence the total number of ways =5!×6!=120×720=86400

In how many ways can $6$ boys and $5$ girls be arranged for group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

Five girls can sit on chairs in a row in $^{5} P_{5} = 5!$ ways.

Also, $6$ boys can stand behind them in a row in $^{6} P_{6} = 6!$ ways.

Hence the total number of ways $= 5! \times 6! = 120 \times 720 = 86400$