In the game of Cribbage, players are each dealt 6 cards from a standard deck of 52 cards. How many different 6-card hands are possible?
Given that
In the game of Cribbage, players are each dealt 6 cards from a standard deck of 52 cards.
Number of cards player deals with = 6
Standard deck of cards contains 52 cards.
We know that
By combinations we can find the number ways of selecting 'r' items from the total 'n' items. = (^{n}C_{r})
How many different 6-card hands are possible?
Here,
n = 52 = Total number of cards
r = 6 = Number of cards to be selected.
By combinations ,
Selecting 'r' items from 'n' available = ^{n}C_{r}
Selecting 6 cards from 52 cards available = ^{52}C_{6}
^{52}C_{6} = $\frac{52x51x50x49x48x47}{6x5x4x3x2x1}$
^{52}C_{6} = 20,358,520 ways.
20,358,520 different 6-card hands are possible .