Question

Eight chairs are numbered $1to8$. Two women and three men wish to occupy one chair each. First, the women choose the chairs amongst the chairs marked 1 to 4 then the men select the chairs amongst the remaining. The number of possible arrangements are:

Answer 1

We have 8 chairs,

First, the women will choose 2 chairs from the available 4,

The possible number of ways for this $=4\ast 3=12$;

The three men will now choose from 6 available chairs,

Hence, possible number of arrangements = ${}^6{\text{C}}_3$$=20$ ;

Hence, required answer = 240.