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# the game of Cribbage, players are each dealt 6 cards from a standard deck of 52 cards.  How many different 6-card hands...

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.   = (nCr)

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 = nCr

Selecting 6 cards from 52 cards available = 52C6

52C6$\frac{52x51x50x49x48x47}{6x5x4x3x2x1}$

52C6 = 20,358,520 ways.

20,358,520 different 6-card hands are possible .

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