Permutations & Combinations Question - None

Question

Match the following columns:

Column I:

(A) Number of increasing permutations of numbers $(a_1, a_2, \ldots, a_n)$, where $a_1 < a_2 < a_3 < \ldots < a_{m-1} < a_m$

(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

(C) Number of ways in which r red balls and $(m-1)$ green balls can be arranged in a line, so that no two red balls are together (balls of the same colour are alike)

(D) Number of ways in which m different toys can be distributed in n children, if every child may receive any number of toys

Column II:

(p) $n^m$

(q) $m C_n$

(r) $n C_m$

(s) $m^n$

Accepted Answer

Analysis:

(A) Choosing m increasing numbers from n set: $n C_m$ ways → (r)

(B) Each of n monkeys chooses from m men independently: $m^n$ ways → (s)

(C) Arrange r red balls and (m-1) green balls with no two red together: $m C_r$ ways → (q)

(D) Each of m toys can go to any of n children: $n^m$ ways → (p)

Question:

Step-by-Step Solution

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