10 different letters of English alphabet are given. Out of these letters, words of 5 letters are for

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6.Permutation and Combination

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$10$ different letters of English alphabet are given. Out of these letters, words of $5$ letters are formed. How many words are formed when at least one letter is repeated

A

$99748$

B

$98748$

C

$96747$

D

$97147$

Solution

(a) Number of words of $ 5$ letters in which letters have been repeated any times =${10^5}$

But number of words on taking 5 different letters out of $10 = {\,^{10}}{C_5} = 252$

Required number of words = ${10^5} – 252 = 99748$.

Standard 11

Mathematics

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