Question

Assertion :The number of different codes formed by three letters of English alphabet followed by a three digit number is $(26{)}^3\times 900$ (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 $n^r$

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

Answer 1

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 $=999-99=900$

Now $3$ letters from $26$ alphabets can be picked up in $26\times 26\times 26$ ways as repetition is allowed.

So total number of codes having $3$ letters of alphabets followed by $3$ digit number are ${26}^3\times 900$

Reason: If $r$ things are to be taken from $n$ different things with repetition allowed, then the number of outputs $=n^r$

This is the correct explnanation of Assertion too.