# What is the probability that all 4 cards have different value?

From a standard deck of 52 cards, 4 cards are chosen without replacement. What is the probability that all the 4 cards have different numerical value?
N.B.-It is assumed that Jacks,Queens, Kings and Aces have numerical values 11,12,13 and 1 respectively.
My solution-After choosing any 1 card, we can choose 48 cards(removing other cards of the same value) out of the remaining 51 cards and so on till we pick 4 cards.Therefore, the required probability is $\frac{52}{52}\times\frac{48}{51}\times\frac{44}{50}\times\frac{40}{49}$.
Kindly verify.

• IMO the approach and the result are correct. – digital-Ink Jun 15 '14 at 14:08
• your way includes order of picking; divide by 4!. – RE60K Jun 21 '14 at 14:43

As remarked in a comment, your calculation is correct. The other comment that says that you should divide by $4!$ is in error.