Multiple choice

There are 13 cards of diamond symbol in a deck, out of which 3 cards are selected at random. How many different ways of selecting 3 cards are there?

  1. 286

  2. 300

  3. 310

  4. 325

  5. 330
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A Correct answer
Explanation

Selecting 3 cards out of 13 is a combination problem: 13C3 = (13 * 12 * 11) / (3 * 2 * 1) = 13 * 2 * 11 = 286.

AI explanation

To find the number of ways to select 3 cards from 13 diamond cards, we use the combinations formula nCr, which is n factorial divided by r factorial multiplied by n minus r factorial. Substituting the values gives 13C3, calculated as 13 factorial divided by 3 factorial multiplied by 10 factorial. This simplifies to 13 multiplied by 12 multiplied by 11, divided by 3 multiplied by 2 multiplied by 1. The result of 1716 divided by 6 is 286.

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