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Question Number 181251 by cortano1 last updated on 23/Nov/22

Commented by cortano1 last updated on 23/Nov/22

$$\mathrm{A}\mathrm{photograph}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{taken}\mathrm{of}\mathrm{seven}\mathrm{girls}$$$$\mathrm{standing}\mathrm{in}\mathrm{two}\mathrm{rows},\mathrm{with}\mathrm{one}\mathrm{row}$$$$\mathrm{in}\mathrm{front}\mathrm{of}\mathrm{the}\mathrm{other}.\mathrm{The}\mathrm{tallest}\mathrm{girl}$$$$\mathrm{must}\mathrm{be}\mathrm{in}\mathrm{the}\mathrm{midlle}\mathrm{of}\mathrm{the}\mathrm{row}\mathrm{of}$$$$\mathrm{three}\mathrm{and}\mathrm{the}\mathrm{shortest}\mathrm{girl}\mathrm{must}\mathrm{be}$$$$\mathrm{in}\mathrm{row}\mathrm{at}\mathrm{the}\mathrm{front}.\mathrm{In}\mathrm{how}\mathrm{many}$$$$\mathrm{ways}\mathrm{can}\mathrm{the}\mathrm{girls}\mathrm{be}\mathrm{arranged}?$$

Answered by mr W last updated on 23/Nov/22

$$case1:$$$$XXXX$$$$STX$$$$\Rightarrow 2\times 5!$$$$case2:$$$$XTX$$$$SXXX$$$$\Rightarrow 4\times 5!$$$$totally:6\times 5!=720ways$$

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