Combinatorics + function = lot of fun

Probability Level 4

Let $A = \{a_1, a_2, \ldots, a_{100}\}$ and $B = \{b_1, b_2, \ldots, b_{50}\}$ be two sets of real numbers.

How many non-decreasing function from $A$ to $B$ are there such that every element of $B$ has an inverse image?

None

^{102}C_{50}

^{149}C_{49}

^{99}C_{50}

^{100}C_{49}

^{100}C_{50}

1 solution

Abdelhamid Saadi
Sep 11, 2015

This problem is equivalent to the number of ordered partition of 100 into 50 parts.

We know that the number of ordered partition of n into k parts is $C_{n-1}^{k-1}$ .