Permutations and Combinations 1 Question 9

9. Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each.

First the women choose the 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) ${ }^{6} C _3 \times{ }^{4} C _2$

(b) ${ }^{4} P _2 \times{ }^{4} P _3$

(c) ${ }^{4} C _2+{ }^{4} P _3$

(d) None of these

(1982, 2M)

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Answer:

Correct Answer: 9. (d)

Solution:

  1. Since, the first 2 women select the chairs amongst 1 to 4 in ${ }^{4} P _2$ ways. Now, from the remaining 6 chairs, three men could be arranged in ${ }^{6} P _3$.

$\therefore$ Total number of arrangements $={ }^{4} P _2 \times{ }^{6} P _3$.



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