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. (c)
Solution:
- 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 $={ }^{4} P _2 \times{ }^{6} P _3$.
