Question

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. $C_3^6\times C_2^4$
• B. $P_2^4\times P_3^4$
• C. $=P_2^4\times P_3^6$$C_2^4\times C_3^4$
• D. None of these.

Answer 1

The correct option is D

None of these.

The explanation for correct option:

Calculate the possible arrangements for women and men separately.

Given: there are $2$ women and they can sit in the chair from $1$to$4$.

The possible arrangements for the women-only is $={}^{4}P_2$.

Now, the remaining chairs$=(8-2)=6$.

Given: $3$ men can sit any of those remaining chairs.

The possible arrangements for the men only is $={}^{6}P_3$.

Therefore, the possible arrangements for both men and women$={}^{4}P_2\times {}^{6}P_3$.

Therefore, Option(D) is the correct answer.