Question

You are given the letters M-A-T-H-I-S-O-N. How many unique 4-letter arrangements are possible?
Should I solve this using 'combination'?

Answer 1

The order of the letters matters. Therefore permutations are needed: 8P4.

Answer 2

well, the order of our letters in each arrangement actually matters i.e. \(M-A-T-H\) and \(H-T-A-M\) are two distinct arrangements (permutations).

Answer 3

indeed, you'd count \(_8P_4=8!/4!=8\times7\times6\times5\)... this actually has a fairly elementary counting explanation. consider the possibilities for each letter:

Answer 4

out of \(\{M,A,T,H,I,S,O,N\}\) we have \(8\) possibilities for our first letter, followed by the remaining \(7\) for our second (arrangement implies we can only use each letter once), etc.