Question

Assertion :The number of permutations of the letters of word ALLAHABAD is 7560. Reason: The number of permutations of n obie where $P_1$ objects are of one kind, $P_2$ are of second ....,$P_k$ are of $k^{th}$ kind & the rest if any, are of different kind is equal to $\frac{n!}{P_1!P_2!....P_k!}$

• 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),

$n=9A=4,L=2$ rest are of different kind

$\therefore$ Required number of ways $=\frac{9!}{4!2!1!1!1!}=\frac{5\times 6\times 7\times 8\times 9}{2}=7560$

Statement B is correct explanation of A