Problema Solution
I have 22 medics in my platoon I have 6 units that each need a medic how many combinations can I send to there respectful units
Answer provided by our tutors
The number of k-permutations of n is P(n,k) = n!/(n - k)!
n = 22, k = 6
P(22, 6) = 22!/(22 - 6)! = 22!/16! = 17*18*19*20*21*22 = 53,721,376
this is the case when we count the cases when one medic goes to different unit, like for example one set of 6 medics can go in 6! different ways to 6 units.
On the other hand the numberof 6-combinations of 22 elements is
C(22, 6) = 22!/(6!(22 - 6)!) = 17*18*19*20*21*22/ 720 = 74,613
this is the case when the order doesn't matter - that is if we pick 6 medics out of 22 then this is counted as 1 way of sending the medics to the 6 units.