Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are spades.
A) $1716$
B) $33,446,140$
C) $4$
D) $5040$
E) $26,545$

Question

Quizplus · Accepted Answer

The number of ways to choose 7 cards out of the 13 spades in a standard deck is calculated using the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items (13 spades), and $k$ is the number of items to choose (7 cards). Thus, $C(13, 7) = \frac{13!}{7!(13-7)!} = 1716$.

Seven Cards Are Chosen at Random from a Standard Deck 171617161716

Seven Cards Are Chosen at Random from a Standard Deck $1716$