Probability hw help math ?

(I’ve attached the photo example of the cards)

Consider the card deck pictured to the right. What is the number of possible

5-card hands that would be classified as a “two-pair?” A two-pair is a hand with 2 cards

of one denomination, 2 cards of another denomination (that is different than

the first denomination), and 1 card that is of a different denomination than both of the

pairs. For example, the hand pictured here is a two-pair.

The order of the cards doesn’t matter when making a hand

Update:

It wouldn’t let me attach the photo but why the example shows is cards in the color and order of (a green 3 a red 3 a yellow 8 a red 8 and a 1 blue) 

1 Answer

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  • 1 month ago
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    My previous answer still applies, if I'm correct about the deck. I'm assuming there are numbers 1 through 9 (values) in 4 "suits" (actually colors).

    STEP 1 - Pick the cards in the pairs

    From the 9 values, pick the 2 values that will make up the two pairs (e.g. 3s and 8s). 

    C(9,2) = (9 * 8) / (2 * 1) = 36 ways to pick the pairs

    STEP 2 - Pick the *colors* for each pair.

    For each value, pick the two colors in that value. 

    C(4,2) = (4 * 3) / (2 * 1) = 6 ways to pick the suit for the lower pair (e.g. red & green)

    C(4,2) = 6 ways to pick the suit for the higher pair (e.g. yellow & red) 

    STEP 3 - Pick the final non-matching card.

    There will be 7 other values in 4 colors (28 cards) left for the non-matching value. So pick one (e.g. blue 1)

    C(28,1) = 28 ways

    STEP 4 - Multiply that all together:

    36 * 6 * 6 * 28 

    Answer:

    36,288 ways to form a "two-pair" hand from a 36-card deck.

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