- #1

Big-Daddy

- 343

- 1

## Homework Statement

A word has

*n*letters, in which one of those letters is present

*a*times and another is present

*b*times (all other letters are present only once).

a.) How many combinations of

*x*letters are there from this word?

b.) How many arrangements of

*x*letters are there from this word?

## Homework Equations

nCr=n!/((n-r)!r!)

nPr=n!(n-r)!

Any others?

## The Attempt at a Solution

I'm not completely clear but I think the problem means, e.g. “POSSESSES”, 5 letters being chosen: n=9, r=5, a=5 (5 Ss), b=2 (2 Es).

I was told the solution would require a sigma function (summation operator) so it won't be easy. So far, for combinations, I came up with something like Ʃ(i=0 to i=n-a-b; C(n-a-b,i)) but now I'm thinking that's only a small piece of the puzzle. Help?