MHT CET · Maths · Permutation Combination
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
- A \(144\)
- B \(362880\)
- C \(2880\)
- D \(1140\)
Answer & Solution
Correct Answer
(C) \(2880\)
Step-by-step Solution
Detailed explanation
\(\frac{M}{1} \frac{W}{2} \frac{M}{3} \frac{W}{4} \frac{M}{5} \frac{W}{6} \frac{M}{7} \frac{W}{8} \frac{M}{9}\)
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 \(=120 \times 24=2880\)
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 \(=120 \times 24=2880\)
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