MHT CET · Maths · Permutation Combination
Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked 1 to 4 , and then the men select the chairs from amongst the remaining. The number of possible arrangements is
- A \({ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2\)
- B \({ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3\)
- C \({ }^4 \dot{C}_2+{ }^4 \mathrm{P}_3\)
- D \({ }^4 \mathrm{P}_2+{ }^6 \mathrm{P}_3\)
Answer & Solution
Correct Answer
(B) \({ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3\)
Step-by-step Solution
Detailed explanation
Two women can be made to sit on chairs marked 1 to 4 in \({ }^4 P_2\) ways and then three men can be seated in 6 available seats in \({ }^6 \mathrm{P}_3\) ways.
\(\therefore\) number of possible arrangements is \({ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3\).
\(\therefore\) number of possible arrangements is \({ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3\).
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