Answer:
604800
Step-by-step explanation:
Given : The ten students in a club are lined up in a row for a group photograph.
To Find: How many different arrangements are possible if the club includes one set of identical triplets wearing matching clothes?
Solution:
The club includes one set of identical triplets wearing matching clothes
So, the remaining students = 10-3 = 7
Now there is an arrangement between these seven students.
Since order has to be maintained .So, we will use permutation
Formula : \(^nP_r=\frac{n!}{(n-r)!}\)
So, \(^{10}P_7=\frac{10!}{(10-7)!}\)
\(^{10}P_7=\frac{10!}{(3)!}\)
\(^{10}P_7= 604800\)
Hence there are 604800 possible arrangements if the club includes one set of identical triplets wearing matching clothes
