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 P1 objects are of one kind, P2 are of second kind, Pk are of k text th kind and the rest, if any, are of different kind is ...B... . Here, A and B refer to

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 P1 objects are of one kind, P2 are of second kind, Pk are of k text th kind and the rest, if any, are of different kind is ...B... . Here, A and B refer to (A) (n !/P ! 2 !), (n !/(P1+P2+ ldots+Pk) !) (B) (n !/P !), (n !/P1 ! P2 ! ldots Pk !) (C) (P !/n !), ((P1+P2 ldots+Pk)/n !) (D) None of these

Tardigrade Admin · Accepted Answer

I. The number of permutations of n objects, where P objects are of the same kind and rest are all different =(n !/P !) II. The number of permutations of n objects, where P1 objects are of one kind, P2 are of second kind,..., Pk are of k text th kind and the rest if any, are of different kind, is (n !/P1 ! P2 ! ldots Pk !)

$\frac{n !}{P ! 2 !}, \frac{n !}{( P _{1} + P _{2} + \dots + P _{k} ) !}$

$\frac{n !}{P !}, \frac{n !}{P _{1} ! P _{2} ! \dots P _{k} !}$

$\frac{P !}{n !}, \frac{( P _{1} + P _{2} \dots + P _{k} )}{n !}$

None of these

P!2!n!​,(P1​+P2​+…+Pk​)!n!​

P!n!​,P1​!P2​!…Pk​!n!​

n!P!​,n!(P1​+P2​…+Pk​)​

None of these

$\frac{n !}{P ! 2 !}, \frac{n !}{( P _{1} + P _{2} + \dots + P _{k} ) !}$

$\frac{n !}{P !}, \frac{n !}{P _{1} ! P _{2} ! \dots P _{k} !}$

$\frac{P !}{n !}, \frac{( P _{1} + P _{2} \dots + P _{k} )}{n !}$