Question

Match the following for a deck of $52$ cards.

• A. $16$
• B. $4$
• C. $12$
• D. $36$

Answer 1

The distribution of cards in each of the four suits (clubs, spades, diamonds and hearts) is shown in the above tree diagram. And, it is very clear that the distribution of cards is uniform across all four suits.

Hence, the numbers of cards in each of the given option types, in a deck of $52$ cards, are shown in the table below:

Cards	Number of cards in one suit	Number of cards in a deck with four suits
Lettered cards	4 (J, K, Q, A)	$4\times 4=16$
Aces	1 (A)	$1\times 4=4$
Face cards	3 (J, K, Q)	$3\times 4=12$
Numbered cards	9 ($2$ to $10$)	$9\times 4=36$