Multiple choice

In a game, a person has to select three cards from a deck of cards. If he selects a face card, then the other two cards also have to be face cards. If a number card is selected, then all the other cards have to of the same number. In how many different ways can the selection be made?

  1. 12C3 + 9 × 4C3

  2. 12C3 + 40C3

  3. 13C3 + 4C3

  4. 12C3 + 9 × 4!

  5. 14C3 + 9 × 4C3
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A Correct answer
Explanation

There are 12 face cards. Selecting 3 face cards is 12C3. For number cards, there are 9 numbers (2-10), each with 4 suits. Selecting 3 cards of the same number is 4C3 for each number, so 9 * 4C3.

AI explanation

A standard deck contains 12 face cards and 40 number cards. To choose three face cards, the number of combinations is 12C3. For the number cards, there are 9 different ranks (Ace through 10) with 4 suits each, and choosing all three cards of the same number can be done in 4C3 ways per rank, yielding 9 multiplied by 4C3 combinations. Adding these independent scenarios gives the total number of valid selections as 12C3 + 9 × 4C3.

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