3-men-and-4-women-are-to-sit-on-a-table-Calculate-the-number-of-possible-sitting-arrangements-if-a-they-sit-in-a-row-such-that-the-men-must-not-sit-next-to-each-other-b-they-

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Question Number 167979 by nadovic last updated on 31/Mar/22

$$3\mathrm{men}\mathrm{and}4\mathrm{women}\mathrm{are}\mathrm{to}\mathrm{sit}\mathrm{on}\mathrm{a}$$$$\mathrm{table}.\mathrm{Calculate}\mathrm{the}\mathrm{number}\mathrm{of}$$$$\mathrm{possible}\mathrm{sitting}\mathrm{arrangements}\mathrm{if}$$$$\left(a\right)\mathrm{they}\mathrm{sit}\mathrm{in}\mathrm{a}\mathrm{row}\mathrm{such}\mathrm{that}\mathrm{the}$$$$\mathrm{men}\mathrm{must}\mathrm{not}\mathrm{sit}\mathrm{next}\mathrm{to}\mathrm{each}$$$$\mathrm{other}.$$$$\left(b\right)\mathrm{they}\mathrm{sit}\mathrm{in}\mathrm{circular}\mathrm{pattern}\mathrm{and}$$$$\mathrm{the}\mathrm{clockwise}\mathrm{and}\mathrm{anticlockwise}$$$$\mathrm{orders}\mathrm{are}\mathrm{considered}\mathrm{the}\mathrm{same}.$$

Answered by mr W last updated on 31/Mar/22

$$\left(a\right)$$$$\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}W\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}W\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}W\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}W\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}$$$$C_5^3\times 3!\times 4!=1440arrangements$$

Commented by mr W last updated on 31/Mar/22

$$\left(b\right)$$$$\frac{(7-1)!}{2}=360$$

Commented by Tawa11 last updated on 01/Apr/22

$$\mathrm{Great}\mathrm{sir}$$

Commented by peter frank last updated on 01/Apr/22

$$\mathrm{what}\mathrm{if}\mathrm{woman}\mathrm{must}\mathrm{not}\mathrm{seat}\mathrm{each}$$$$\mathrm{other}$$

Commented by mr W last updated on 01/Apr/22

$$WMWMWMW$$$$3!\times 4!=144arrangements$$

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