Easy Permutation-Combination Solved QuestionAptitude Discussion

 Q. Ten different letters of alphabet are given, words with 5 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. 99748 ✖ D. 42386

Solution:
Option(A) is correct

Number of words which have at least one letter replaced:

$= \text{Total number of words - total number of words in which no letter is repeated}$

$⇒{10}^5 – {^{16}P_5}$

$⇒100000 - 30240$

$= 69760$

(3) Comment(s)

V J
()

$Explanation:$

Number of words which have at least one letter replaced= Total number of words x Total number of words without repetition of letters

Now,

Total number of words= 10x10x10x10x10= 10^5

And,

Total number of words without repetition of letters

= 10x9x8x7x6

= {10}^5 – {^{10}P_5}

=30240

Hence, $100000-30240=69760$

Kamal
()

Please correct the solution it would be

${10}^5 - ^{10}P_5$

ABHIJEET
()