Maths-
General
Easy

Question

# Eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from the remaining. The number of possible arrangements is-

Hint:

## The correct answer is: None of these

### DETAILED SOLUTIONNow, we have been given 8 chairs which are numbered from 1 to 8. Also, it has been given that women choose the chairs from amongst the chairs marked 1 to 4, and then men select from remaining chairs. In total there are 2 women and three men who wish to occupy one chair each.Now, we know the number of ways of selecting r objects among n is . So, we have the ways in which we can choose two chairs among four numbered 1 to 4 is  and we can arrange the women then in 2! ways. Also, we have the ways of selecting 3 chairs among the rest 6 chairs is  and in them we can permute the men in 3! ways.So, in total we have number of possible arrangements as, 2!   3!Now, we know that   = Therefore, we have,Total ways =

It is important to note that we have used a fact that  = . This can be understood as we know that  = and  =   . So, substituting this we have  =  .