Question

10 different letters of an alphabet are given words with 5 letters are formed from these given letters then the number which have atleast one letter repeated is

• A. $69740$
• B. $30240$
• C. $99748$
• D. None of these

Answer 1

Answer: (A)

$69740$

$10$ different letters -$5$ words.

no. of $5$ letters words when repetition allowed

$={10}^5=100000$

no. of word with atleast $1$ letter repeated = [no. of $5$ letters word when allowed]-[no. of $5$ letters words when repetition not allowed]

no. of $5$ letters words when repetition not allowed =${}^{10}{C}_5\times \Rightarrow \frac{10!}{5!}\Rightarrow 10\times 9\times 8\times 7\times 6$

$\Rightarrow 30240$

$\therefore$ no. os words with atleast $1$ letter repeated $={10}^5-30240$

$=69740$