Kelvin the frog jumps along the number line starting at 0 . Every time he jumps, he jumps either one unit left or one unit right. For example, one sequence of jumps might be $0 \rightarrow-1 \rightarrow 0 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 2$.

How many ways are there for Kelvin to make exactly 10 jumps and land on a prime number? (The prime numbers are the sequence $2,3,5,7, \ldots$ Negative numbers are not considered prime.)
First, note that every time Kelvin jumps, he must jump from an even number to an odd one or vice-versa. Thus after ten jumps, he must land on an even number. So, if that number is to be prime, it must be 2 .

This means Kelvin must make 6 jumps right and 4 jumps left. That means the answer is $\left(\begin{array}{c}10 \\ 6\end{array}\right)=210$.