10 different letters of English alphabet are given. A word is formed using 5 letters ( with replacement ) out of these. Find the probability that at least one letter is repeated in the word. Choose the most appropriate option:
A) (10^5 - 10P5 ) / 10^5
B) (10P5 ) / 10^5
C) (10^5 - 10P5 ) / 10
D) None of these
E) Cannot be determined
Explanation :   Without restriction,   No. of arrangements of 5 letter out of 10 different letters = 10(5).   To find at least one, it is better to find the probability of the complement of the event (no letter is repeated).   No. of arrangements of 5 letters ( out of 10) without repetition = 10P5.   =&gt; P (no letter is repeated)   = 10P5 / 10(5) .   =&gt; P ( at least one letter is repeated )   = 1 - ( 10P5 / 10(5) ).   Hence, the required probability is (105 - 10P5 ) / 10(5)   (10^5 - 10P5 ) / 10^5nswer : (10^5 - 10P5 ) / 10^5
<result>A</result>
10 different letters of English alphabet are given. A word is formed using 5 letters ( with replacement ) out of these. Find the probability that at least one letter is repeated in the word.