probability and permutations

Question

The 10 letter tiles S A C D E E M I I and O are in a bag. What is the probability that the letters 

S A M E will be drawn from the bag in that order?

Answer 1

The probability of drawing an s first is 1/10

Once this has occurred there are nine tiles left so the probability of drawing an a is 1/9

next the probabilty of drawing an m is 1/8 and lastly the probability of drawing an e is 2/7(there are 2 e tiles in the bag)

For all these events to occur you have to multiply so the probability is

(1/10) x (1/9) x (1/8) x (2/7) =2/5040 or 1/2520