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Assertion :The number of different codes formed by three letters of English alphabet followed by a three digit number is (26)3×900 (if repetitions are allowed) Reason: The number of permutations of n different things taken r at a time when each thing may be repeated.any number of times is nr

A
Both (A) & (R) are individually true & (R) is correct explanation of (A),
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B
Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
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C
(A)is true but (R) is false,
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D
(A)is false but (R) is true.
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Solution

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),
Assertion: Codes are to be formed by 3 letters of English alphabet followed by 3 digit number.
So no of 3 digit numbers =99999=900
Now 3 letters from 26 alphabets can be picked up in 26×26×26 ways as repetition is allowed.
So total number of codes having 3 letters of alphabets followed by 3 digit number are 263×900
Reason: If r things are to be taken from n different things with repetition allowed, then the number of outputs =nr
This is the correct explnanation of Assertion too.

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