It is required to seat 5 men and 4 women in a row so that the men occupy odd places. Then the number of…

It is required to seat 5 men and 4 women in a row so that the men occupy odd places. Then the number of arrangements that are possible is
  1. $144$
  2. $362880$
  3. $2880$
  4. $1140$

Solution

$\frac{M}{1} \frac{W}{2} \frac{M}{3} \frac{W}{4} \frac{M}{5} \frac{W}{6} \frac{M}{7} \frac{W}{8} \frac{M}{9}$ 5 men can be seated in 5 odd places in $5_{\mathrm{P}_5}=120$ ways and 4 women can be seated in remaining 4 places in $4_{p_4}=24$ ways $\Rightarrow$ Total possible arrangements $=120 \times 24=2880$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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