Q.
Match the column :
Column I
Column II
A
Number of increasing permutations of $m$ symbols are there from the $n$ set numbers $\left\{a_1, a_2, \ldots, a_n\right\}$ where the order among the numbers is given by $a_1
P
(P) $n^m$
B
There are $m$ men and $n$ monkeys. Number of ways in which every monkey has a master, if a man can have any number of monkeys
Q
${ }^{ m } C _{ n }$
C
Number of ways in which $n$ red balls and $( m -1)$ green balls can be arranged in a line, so that no two red balls are together, is (balls of the same colour are alike)
R
${ }^n C_m$
D
Number of ways in which ' $m$ ' different toys can be distributed in ' $n$ ' children if every child may receive any number of toys, is
S
$m ^{ n }$
| Column I | Column II | ||
|---|---|---|---|
| A | Number of increasing permutations of $m$ symbols are there from the $n$ set numbers $\left\{a_1, a_2, \ldots, a_n\right\}$ where the order among the numbers is given by $a_1| P |
(P) $n^m$ |
|
| B | There are $m$ men and $n$ monkeys. Number of ways in which every monkey has a master, if a man can have any number of monkeys | Q | ${ }^{ m } C _{ n }$ |
| C | Number of ways in which $n$ red balls and $( m -1)$ green balls can be arranged in a line, so that no two red balls are together, is (balls of the same colour are alike) | R | ${ }^n C_m$ |
| D | Number of ways in which ' $m$ ' different toys can be distributed in ' $n$ ' children if every child may receive any number of toys, is | S | $m ^{ n }$ |
Permutations and Combinations
Solution: