# Thread: a hand of 13 cards ...

1. ## a hand of 13 cards ...

a hand of 13 cards are chosen at random from a deck of 52 playing cards. What is the probability that a hand is void in at least one suit.

Hint: Note that the answer is not (4 1)(39 13) / (52 13)

Thank you so much

2. Originally Posted by sabrina87
a hand of 13 cards are chosen at random from a deck of 52 playing cards. What is the probability that a hand is void in at least one suit.

Hint: Note that the answer is not (4 1)(39 13) / (52 13)

Thank you so much
Well, lets do the calculation for void in hearts.

The number of ways of selecting a hand of $13$ cards void in hearts is $39 \times 38 \times ... \times 27$ $=\frac{39!}{26!}
$
(we can divide by $13!$ if we wish to not distinguish between permutations, but we don't need to here)

So the number of ways of selecting a hand void in some suit is $4 \times \frac{39!}{26!}$

The total number of hands is $\frac{52!}{39!}$

The probability you seek is the ratio of these.

CB