I have been given a question about (i think) permutations, it asks to find how many x letter sequences can be made out of a word. I am getting confused because it first asks how many different sequences and then it asks how many different 'sets' can be made, and i cannot destinguish the difference between the two using the permutation formula.
(1) How many 3 letter sets can be selected from the letters m, a, t, h, s?
it also gives a condition (must contain letter m) can this be done using the formula?
(2) How many 4 letter sequences are possible that use the letters m, a, t, h, s at most once each and contains the letter m?
and lastly a few of the questions say "at most once each" and some just say "once each" should the "at most once each" just be referring to they cannot repeat at all? and how would this be different from calculating normal permutations?
Best Answer
For 1, without the condition you can select $5 \choose 3$ sets. If $m$ has to be included, you can select $4\choose 2$ for the other letters. When you talk of sequences, you care about order. The easiest way for this is to calculate the total number of sequences, then subtract the ones that don't have $m$ in them somewhere. Choosing a sequence of four items out of five, you have five choices for the first, four for the next, etc. so there are 5*4*3*2=120. Without $m$ you have 4*3*2*1=24,so the ones that have $m$ are $96$ Your last is English, not Math, but yes "at most once" means you cannot repeat.