How many 100-digit numbers' sums of digits equal 3? How many 100-digit numbers' sums of digits equal 3? How do I solve this?

We have a few possibilities.
A 1 with two other ones somewhere. $99\choose{2}$ 
A 1 with a two somewhere else $99\choose{1}$
A 2 with a one somewhere else $99\choose{1}$
A 3 with 99 zeroes $1\choose{1}$
$${99\choose2} + {99\choose1} + {99\choose1} + {1\choose1} = 4851 + 99 + 99 + 1 = 5050$$
