Hello,

1 card of a given value :

52 possibilities

Then remain 51 cards, including 3 of this value.

Another card of this value :

3 possibilities (because there are 3 left of this value).

There are 50 cards remaining. But we're only interested in 48 of them since we don't want to have the first value anymore.

1.

48 possibilities.

There remain 47 cards, including 3 of the value1., which we are not interested in because we want them to be different.

2.

44 possibilities (47-3)

The same way, there remain 40 cards which do not contain the previous values.

3.

40 possibilities.

---> Number of possible combinations : 52x3x48x44x40

I hope my reasoning seems correct to you :x