Father mother, 2 boys and 3 girls are asked to line up for photograph. determine the number of ways
(i) if no restrictions,
(ii) parents stand together,
(iii) parents do not stand together and
(iv) all females together.

Solution(By Examveda Team)

(i) if no restrictions, n!
n(number of member) = 1+1+2+3 = 7
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
= 5040

(ii) parents stand together,
Grouping parents we will create a m and a n
m = parents together = 2
n = order of the photograph = 6
mn = 2! 6! = 1440

(iii) parents do not stand together
parents don't stand together = total – stand together
parents don't stand together = 5040 – 1440
parents don't stand together = 3600

(iv) all females together
Grouping women we will create a m and a n
m = grouping women together = 4
n = order of the photograph = 4
mn = 4! 4! = 576