Permutations and Combinations

The letters of the word POSSESSES are written on nine cards, one on each card. The cards are shuffled and four of them are selected and arranged in a straight line.
a)How many possible selections are there of four letters?
b)How many arrangments are there of four letters?

I would like to ask if there is a good way to do this question besides listing all the possible selections(part a) and rearrange all the possible selections(part b)? Which method should we use for the exam?

a)
SSSS SSSO SSSP SSSE
SSEE SSEO SSOP SSEP
SOEE SPEE OEEP
POSE

There are 12 possible selections.

b) Arranging all the possible selections gives
4! + 6(4!/2!) + (4!/2!2!) + 3(4!/3!) + (4!/4!)
=115

Is there any other way besides this? Thank you.

Reply 1

Simba

If you have a calculator, try using the buttons nCr and nPr ^_^ ... They're designed for combinations and permutations I believe, though I've never used them myself.

Reply 2

Sol-Badguy

Simba

If you have a calculator, try using the buttons nCr and nPr ^_^ ... They're designed for combinations and permutations I believe, though I've never used them myself.

Thanks for giving your thought. But what you have said is not suitable here. There are 5 S's and two E's. If it was only the word POSE and you are asked to choose 2 letters from it, then it is 4C2. If you are asked for the arrangements for the 4 letters then it is 4! or 4P4 which is the same.