Letters in the word UNIVERSITY: E, I,N,R,S,T,U,V,Y

There are 9 distinct letters. Let us say that each letter is used only once in formation of words of any length. Let P(m, n) denote the number of permutations of selecting n items from m, ie., m! / (m-n)!

__1. Number of 9 letter words__:

If all 9 letters are to be used: 9 !

2. **If words contain 0 to 9 letters:** Sum P(9, n) with n denoting the number of letters to be present in the word.

P(9,0) + P(9,1)+ P(9,2) + P(9,3) +.... + P(9,8) + P(9,9)

(1) + (9) + (9*8) + (9*8*7) + (9*8*7*6) +.....(9!/3!) + (9! /2! )+ (9!/1!) + 9!

please calculated the sum.

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If you are looking for formation of 8 letter words: P(9,8) = 9!/1! = 9!