Multiple choice

From a well shuffled pack of $52$ playing cards, four are drawn at random. The probability that all are spades, but one is a king is:

  1. $\dfrac{{^{39}{C_4}}}{{^{52}{C_4}}}$
  2. $\dfrac{{^{12}{C_3}}}{{^{52}{C_4}}}$
  3. $ - \dfrac{{^{39}{C_4}}}{{^{52}{C_4}}}$
  4. $\dfrac{{^{12}{C_4}}}{{^{52}{C_4}}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to choose 4 cards is 52C4. We want 4 spades, but one must be a king. There is only 1 king of spades. So we must pick the king of spades (1C1) and 3 other spades from the remaining 12 spades (12C3). Probability = 12C3 / 52C4.

AI explanation

The total number of ways to draw four cards from a deck of 52 is 52C4. Since we need exactly one card to be the king of spades, we select it in 1C1 ways. The other three cards must be spades from the remaining 12 spades, giving 12C3 combinations. The probability is the product of these selections divided by the total combinations, which equals 12C3 / 52C4.

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