Question

"From a standard deck of cards, find the number of different 5-card hands that are made up of 3 spades and 2 diamonds"

Answer 1

`^(13)C_3 * ^(12)C_2 = 22308`

Explanation:

We have 5 spaces. In our hand.

_ _ _ _ _

a standard deck of 52 cards contains 13 cards for each suit.

so we have 13 spades and 13 diamonds in total. There arrangements don't matter (it doesn't matter if the first card is 9 of spades or the second is 9 of spades, all of these will be counted as one arrangement)

`^(13)C_3`: to choose the 3 spade card from a total of 13 spades.

`^(12)C_2`: to choose the 2 diamond cards from a total of 13 diamonds.

and that is it!

we're gonna multiply the two values.

`^(13)C_3 * ^(12)C_2`