Multiple choice

From a deck of 52 playing cards, including 4 aces, a player randomly draws 7 cards without replacement. What is the probability that exactly 2 of the seven drawn cards are aces and the remaining 5 cards are non-ace cards?

  1. 4 C 2 + 48 C 5 52 C 7

  2. 4 C 2 × 48 C 5 52 C 7

  3. 7 C 2 + 48 C 5 52 C 7

  4. 7 C 2 × 48 C 5 52 C 7

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Choose exactly 2 of the 4 aces and 5 of the 48 non-aces, then divide by the total number of 7-card hands. The probability is C(4,2) x C(48,5) / C(52,7), corresponding to option B.

AI explanation

Using the combination formula for independent selections, we multiply the ways to choose exactly 2 aces from the 4 available by the ways to choose exactly 5 non-aces from the 48 available. This gives 4C2 times 48C5 favorable outcomes. We then divide this by the total ways to draw 7 cards from 52, which is 52C7, resulting in the probability (4C2 times 48C5) / 52C7.

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