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 $\displaystyle 13$ cards void in hearts is $\displaystyle 39 \times 38 \times ... \times 27$ $\displaystyle =\frac{39!}{26!}$(we can divide by $\displaystyle 13!$ 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 $\displaystyle 4 \times \frac{39!}{26!}$

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

The probability you seek is the ratio of these.

CB