Question

Fill in the blanks.
I. The number of permutations of $n$ objects, where $P$ objects are of the same kind and rest are all different equals ...A....
II. The number or permutations of $n$ objects, where $P_1$ objects are of one kind, $P_2$ are of second kind, $P_k$ are of $k^{\text {th }}$ kind and the rest, if any, are of different kind is ...B... .
Here, A and B refer to

• A. $\frac{n !}{P ! 2 !}, \frac{n !}{\left(P_1+P_2+\ldots+P_k\right) !}$
• B. $\frac{n !}{P !}, \frac{n !}{P_{1} ! P_{2} ! \ldots P_{k} !}$
• C. $\frac{P !}{n !}, \frac{\left(P_1+P_2 \ldots+P_k\right)}{n !}$
• D. None of these

Answer 1

Answer: (B)

I. The number of permutations of $n$ objects, where $P$ objects are of the same kind and rest are all different $=\frac{n !}{P !}$
II. The number of permutations of $n$ objects, where $P_1$ objects are of one kind, $P_2$ are of second kind,..., $P_k$ are of $k^{\text {th }}$ kind and the rest if any, are of different kind, is $\frac{n !}{P_{1} ! P_{2} ! \ldots P_{k} !}$