Q. 25.0( 1 Vote )

# How many words can be formed using the 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.

Answer :

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

There are 9 distinct letters (’I’ is repeated once).

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)!

(i) If all 9 letters are to be used = 9!

(ii) 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)

= 986410

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Which of the following are true :

(2 + 3)! = 2! + 3!

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