Multiple choice

In shuffling a pack of cards; four are accidently dropped; find the chance that the missing cards should be one from each suit.

  1. $\displaystyle 1-\frac{\left ( 13 \right )^{4}}{^{52}C_{4}}$
  2. $\displaystyle \frac{\left ( 13 \right )^{4}}{^{52}C_{4}}$
  3. $\displaystyle \frac{\left ( 12 \right )^{4}}{^{52}C_{4}}$

  4. none of these
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B Correct answer
Explanation

The total number of ways to choose 4 cards from 52 is 52C4. The number of ways to choose one card from each of the 4 suits is 13 * 13 * 13 * 13 = 13^4.

AI explanation

Using the combination formula, the total number of ways to drop four cards from a pack of 52 is 52C4. To find the favorable ways where one card is from each suit, we select one card from the 13 cards of each of the four suits, yielding 13 x 13 x 13 x 13 combinations. The required probability is calculated by dividing the favorable outcomes by the total outcomes, which gives (13)^4 / 52C4.

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