Eight chairs are numbered 1 to 8. Two women and three m... | Permutations and Combinations (Mathematics)

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

\ ^{6}C_{3} \times \ ^{4}C_{2}

\ ^{4}P_{2} \times \ ^{6}P_{3}

\ ^{4}C_{2} + \ ^{4}P_{3}

None of these

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Correct Answer:

\ ^{4}P_{2} \times \ ^{6}P_{3}

Explanation

From the 1st 4 chairs numbered 1 to 4,2 woman may be seated in

\ ^{4}P_{2}

ways.

\\

Now there are 6 chairs for 3 men and they may seated in

\ ^{6}P_{3}

ways.

\\

\therefore

Total number of arrangements of 2 women and 3 men in 8 chairs with women in 1st 4 chairs

= \ ^{4}P_{2} \times \ ^{6}P_{3}

Explanation

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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