Question

Assertion :$60$ different permutation can be made by the letter of the word $BANANA.$ Reason: The number of permutations of $n$ things of which $p$ are alike of one kind, $q$ are alike of the second kind and the remaining all are distinct is $\frac{n!}{p!q!}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Clearly, there are six letters in the word BANANA of which three are alike of one kind $\left(3A^{\prime }s\right)$, two are alike of second kind $\left(4N^{\prime }s\right)$ and one of its own kind.

Total number of permutations $=\frac{6!}{3!2!}=60$, which follows from Statement $2.$