# How many words can be formed using letter of UNIVERSITY using each letter at most once? i) If each letter must be used, ii) If some or all the letters may be omitted.

1
by Mecrin
sorry i have written wrong
10c3*7! or 10c7*7! is for seven letter words
NO of =& letter word=10C3*7!
please replay me fast!!!! today itself i want thAT !!
i told yu naa you are correct...NO of =& letter word=10C3*7!

2015-10-07T16:46:30+05:30

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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!