Question

There are $m$ men and $n$ monkeys $(n>m)$. If a man can have any number of monkeys, in how many ways may every monkey have a master?

• A. $n^m$ ways
• B. $n^n$ ways
• C. $m^n$ ways
• D. $m^m$ ways

Answer 1

Answer: (C)

$m^n$ ways

Number of men$=m$ and number of monkeys $=n$
Also n>m.
For each of $n$ monkeys the choice of masters is $m$.
hence total number of ways in which every monkey has a master$=\left(\begin{array}{c}m\\ 1\end{array}\right)\left(\begin{array}{c}m\\ 1\end{array}\right)\left(\begin{array}{c}m\\ 1\end{array}\right).......n-times=m^n$