Question

How many 3 letter words can be formed from the word how using the generating function?

Answer 1

You can also split it into specific cases, which would probably be easier. Consider the 3-perms of MII, MSS, MPP, MIS, MIP, SSS, III, PPS, PSS, etc. (Not sure if I got them all.) Then you can use the formula

n!n1!n2!⋯nk!

where ∑k≤nnk=n, for each specific case