m to n
Partial function is map from subset of m to n...
Suppose size of subset is k and k is always 0<=k<=n and there are n^k such mapping are possible...
Now there are mCk possible subsets are of size k..
So from this we can find total no of partial functions..
= mC0 *n^0 + mC1 * n^1 +....+mCm *n^m
= (1+n)^m
Let's take m=2 and n=3
So =2c0 *3^0 + 2c1*3^1 + 2c2 * 3^2
= 1+6+9 = 16
That is (n+1)^m = (3+1)^2 = 16