Question

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is A

52 cards in a deck has 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

Remaining cards in the deck= 52 -4 = 48

Fifth card - any card in the deck = ${}^{48}{C}_1$

Sixth card - any card in the deck = ${}^{47}{C}_1$

Total number of ways $=13\times 13\times 13\times 13\times 48\times 47={13}^4\times 48\times 47$