Five cards are dealt from a pack of cards. What is the probability that they form a straight i.e. they are in sequence ? (For example A,2,3,4,5 or 2,3,4,5,6 or say 8,9,10,J,Q. The ace can be low too for example 10,J,Q,K,A is valid; but say J,Q,K,A,2 is not valid). Note that the order of drawing the cards doesn't matter, we can draw the cards in any order and then shuffle to see whether they can be made into a sequence or not.
My try : To get any valid sequence, say A,2,3,4,5; A have four choices (there are four aces), so does 2 and so on. So any valid string can appear in $4^5$ ways. And from A,2,3,4,5 to 10,J,Q,K,A; there are 10 such possible strings, hence $10\times4^5$ is the no. of favorable ways.
Hence the probability is $10\times 4^5/{52 \choose 5}$.
Am I correct ?
Please help