9 clubs question--8.2

Question

In how many ways can a hand of 9 clubs be chosen from an ordinary deck?

Answer 1

You can count the number of ways to choose a subgroup from a large group using the combination function:

_nC_x = n! / (n-x)! x!

 

There are ₁₃C₉ ways to select 9 clubs from the whole suit of 13 clubs. There are ₅₂C₉ ways to choose 9 cards from the entire deck.

 

₅₂C₉ / ₁₃C₉ is the number of ways of choosing 9 cards of a single suit from the deck.