Permutation-Combination
Aptitude

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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

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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
 ()

calculate your answer on the google calculator..both the solutions given are wrong