Question

In how many ways can one choose 4 cards from a normal deck of cards so as to have all suits present?

• A. (13⁴) x 48 x 47
• B. (13⁴) x 27 x 47
• C. ⁴⁸C₆
• D. 13⁴
• E. (13⁴) x ⁴⁸C₆

Answer 1

The correct option is D

13⁴

52 cards in a deck -13 cards per suit

First card - let us say from suit hearts = ${}^{13}{C}_1$ =13

Second card - let us say from suit diamonds = ${}^{13}{C}_1$ =13

Third card - let us say from suit spade = ${}^{13}{C}_1$ =13

Fourth card - let us say from suit clubs = ${}^{13}{C}_1$ =13

Total number of ways = 13 * 13 * 13 * 13 = ${13}^4$