Question

I have a standard deck of playing cards in one pile, and a deck of 10 distinct Pokémon cards in another

pile. If I randomly choose 3 playing cards and 4 Pokémon cards (and I don't care about the order I draw
them), how many different choices could I make?

Answer 1

You could make 4,641,000 different choices.

Explanation:

The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

How many different choices could I make?

3 cards from a set of 52(number of cards on a standard deck).

4 Pokemon cards from a set of 10. So

`T = C_(52,3)*C_(10,4) = (52!)/(3!49!)*(10!)/(4!6!) = 22100*210 = 4641000`

You could make 4,641,000 different choices.