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?

Respuesta :

Answer:

You could make 4,641,000 different choices.

Step-by-step 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:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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

[tex]T = C_{52,3}*C_{10,4} = \frac{52!}{3!49!}*\frac{10!}{4!6!} = 22100*210 = 4641000[/tex]

You could make 4,641,000 different choices.