My question is this: A company has 15 applicants to interview, and 3 are to be invited on each day of the working week. In how many ways can the applicants be scheduled?
->SO this the formula being used; whn a total of n balls are to be put into k boxes with the conditions that there will be n1 balls in box 1, n2 balls inbox 2, and so on, with nk balls being placed in box k (n1 +···+nk =n) the number of doing this is: n!/{n1!×···×nk!}, with which I obtain 168168000 which is correct but my question is;
-> why aren't we accounting for the fact that the interview can be on any day of the week? like the days of the week listed are: s_ m_ t_ w_ t_ f_ s_ so if I put 3 candidates each in S,M,T,W,T I satisfy the conditions of the formula, but then why not account for the remaining 2 days? Shouldn't I multiply by 3! by considering S,M,T,W,T as a single unit and T,F separate to get the schedules in ANY day of the week?
For the purposes of the problem, the other two days don't exist. It said working week.