What is the number of mappings? It is given that there are two sets of real numbers $A = \{a_1, a_2, ..., a_{100}\}$ and $B= \{b_1, b_2, ..., b_{50}\}.$ If there is a mapping $f$ from $A$ to $B$ such that every element in $B$ has an inverse image and
$f(a_1)\leq f(a_2) \leq ...\leq f(a_{100})$ 
Then, what is the number of such mappings?
I have started tackling the problem by supposing that $b_1<b_2<...<b_{50}$ and dividing elements $a_1, a_2, ..., a_{100}$ in $A$ into $50$ nonempty groups according to their order. Now the problem is... How do I compute the number of mappings defined as $f: A\rightarrow B$ given the observations above?

HINT:
Suppose $f(a_1)=b_{51},$ then there is only $1$ such mapping.
Suppose $f(a_1)=b_{50},$ then there are $\dbinom{50}{1}=50$ such mappings.
Suppose $f(a_1)=b_{49},$ then there are $\dbinom{51}{2}=1275$ such mappings. 
Can you see a pattern!
