To find the probability of selecting 3 hearts and 2 clubs from a standard deck of 52 cards, follow these steps:

1. Determine the total number of ways to draw 5 cards from a deck of 52. This is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. So, the total number of ways to draw 5 cards from 52 is C(52, 5) = 2,598,960.

2. Determine the number of ways to draw 3 hearts from the 13 in the deck. This is given by C(13, 3) = 286.

3. Determine the number of ways to draw 2 clubs from the 13 in the deck. This is given by C(13, 2) = 78.

4. The number of favorable outcomes (drawing 3 hearts and 2 clubs) is the product of the two previous steps. So, there are 286 * 78 = 22,308 ways to draw 3 hearts and 2 clubs.

5. The probability of drawing 3 hearts and 2 clubs is the number of favorable outcomes divided by the total number of outcomes. So, the probability is 22,308 / 2,598,960 = 0.00858, or about 0.86%.

Question

To find the probability of selecting 3 hearts and 2 clubs from a standard deck of 52 cards, follow these steps:

1. Determine the total number of ways to draw 5 cards from a deck of 52. This is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. So, the total number of ways to draw 5 cards from 52 is C(52, 5) = 2,598,960.

2. Determine the number of ways to draw 3 hearts from the 13 in the deck. This is given by C(13, 3) = 286.

3. Determine the number of ways to draw 2 clubs from the 13 in the deck. This is given by C(13, 2) = 78.

4. The number of favorable outcomes (drawing 3 hearts and 2 clubs) is the product of the two previous steps. So, there are 286 * 78 = 22,308 ways to draw 3 hearts and 2 clubs.

5. The probability of drawing 3 hearts and 2 clubs is the number of favorable outcomes divided by the total number of outcomes. So, the probability is 22,308 / 2,598,960 = 0.00858, or about 0.86%.

Knowee AI · Accepted Answer

To find the probability of selecting 3 hearts and 2 clubs from a standard deck of 52 cards, follow these steps:

1. Determine the total number of ways to draw 5 cards from a deck of 52. This is given by the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. So, the total number of ways to draw 5 cards from 52 is C(52, 5) = 2,598,960.

2. Determine the number of ways to draw 3 hearts from the 13 in the deck. This is given by C(13, 3) = 286.

3. Determine the number of ways to draw 2 clubs from the 13 in the deck. This is given by C(13, 2) = 78.

4. The number of favorable outcomes (drawing 3 hearts and 2 clubs) is the product of the two previous steps. So, there are 286 * 78 = 22,308 ways to draw 3 hearts and 2 clubs.

5. The probability of drawing 3 hearts and 2 clubs is the number of favorable outcomes divided by the total number of outcomes. So, the probability is 22,308 / 2,598,960 = 0.00858, or about 0.86%.

Find the probability of selecting 3 hearts and 2 clubs?

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