Question

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of `m/n` is ____

Answer 1

Correct Answer - 5
Here, `___B_(1) ___B_(2) ___B_(3) ___B_(4) ___B_(5)___`
Out of 5 girls, 4 girls are together and 1 girl is separate. Now, to select 2 positions out of 6 positions between boys `= ""^(6)C_(2)" " …(i)`
4 girls are to be selected out of `5 = ""^(5)C_(4) " "..(ii)`
Now, 2 groups of girls can be arranged in `2!` ways. ...(iii)
Also, the group of 4 girls and 5 boys is arranged in `4! xx 5!` ways . `" "...(iv)`
Now, total number of ways `= ""^(6)C_(2) xx ""^(5)C_(4) xx 2! xx 4! xx 5!`
[from Eqs. (i), (ii), (iii) and (iv)]
`therefore " " m = ""^(6)C_(2) xx ""^(5)C_(4) xx 2! xx 4! xx 5!`
and `n = 5! xx 6!`
`rArr " " m/n = (""^(6)C_(2) xx ""^(5)C_(4) xx 2! xx 4! xx 5!)/(6! xx 5!) = (15 xx 5 xx 2 xx 4!)/(6 xx 5 xx 4!) = 5`