Question

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is?

• A. $69760$
• B. $30240$
• C. $99784$
• D. $75600$

Answer 1

Answer: (D)

$75600$

No. of ways to select $5$ letters$=C_5^{10}$

No. of ways to select the repetition letter $=C_1^5$

Permutations$=\frac{5!}{2!}$

So, no. of permutations$=C_5^{10}\times C_1^5\times \frac{5!}{2!}=75600$