Question

Ten different letters of alphabet are given. Words with four letters are formed from these letters, then the number of words which have at least one letter repeated is -

• A. ${10}^4$
• B. ${}^{10}{P}_4$
• C. ${}^{10}{C}_4$
• D. 4960

Answer 1

The correct option is D 4960

We have to form words with 4 letters from 10 letters.

Given, repetition is allowed.

So, total number of words = $10\times 10\times 10\times 10={10}^4$

Number of words without repetition$=10\times 9\times 8\times 7=5040$

Number of word with at least one letter repeated$=10000-5040=4960$