In how many ways can the team members be arranged for the team picture if all the males are always together and if the team comprises of 7 males and 6 females?
Answers
The options for this question are missing: Following are the options:
a) 13!
b) 7! 7!
c) 7! 6!
d) 14!
The correct answer for this question is 7!7!
We will consider all the males as 1 in order to get this response.
In order to understand let us assume all the males to be one quantity because they are going to be always together, and also for the ease of arrangement purpose.
So we have a total of:
where, ‘!’ = Factorial
N! = (N-1)* (N-2)*(N-3)*(N-4)…...3*2*1
0! = 1
Female = f, Male = m, group = g (taken males as one quantity)
6 female + 1 male group = 7
Thus arrangements will be like this:
ffffffg | fffffgf | ffffgff ……… so on
Total arrangements with female = 7!
Now within the group the males could sit in any arrangement.
So this arrangement will be:
g = (m1 m2 m3 m4 m5 m6 m7)
g = (m1 m2 m3 m4 m5 m7 m6)
g = (m1 m2 m3 m4 m6 m5 m7)
….so on
Thus total arrangements within the male group = 7!
So, there are no other arrangements left, thus the final answer will be:
Arrangement1 * Arrangement2 = 7! * 7!