# probability of 4 of a kind from a deck of 52

5 cards from a deck of 52 , how many ways of four of a kind can be dealt ?

I have (13c1) to determine the rank of card

so (13c1)(4c4) is all i can think of until now

can someone explain how does this work ?

There are indeed $\binom{13}{1}$ ways of choosing the kind we have $4$ of. And once that is done, that part of the hand is determined. But then there is the useless fifth card, which can be chosen in $\binom{48}{1}$ ways.
So the number of $4$ of a kind hands is $(13)(48)$. For the probability, divide by $\binom{52}{5}$.
Remark: The person who did the counting you quote did it in I think less clear way. The $4$ of a kind hand will have two denominations, which can be chosen in $\binom{13}{2}$ ways.
For each choice, we have $2$ choices as to which denomination we will have $1$ of. And then the actual card can be chosen in $\binom{4}{1}$ ways, for a total of $2\binom{13}{2}\binom{4}{1}$.