Probability Distribution

The question is three integers are selected at random from the set (1,2,...,10). What is the probability that the largest of these is less than or equal to 5?

Without replacement, each number has the same probability to being picked. Three numbers have to picked and the must all be under 5 (because the largest has to be 5, or less than 5). So the first number has 5 choices (1 through 5), the second number has to still be less than 5 and has 4 choices (1 through 5 minus number just picked), the last number has 3 choices (1 through 5 minus 2 numbers chosen).

5x4x3=60, So there's 60 different combinations of integers.
I'm thinking that there's 1 through 10 for numbers, there can be 10 options for the first number, 9 for second, 8 for third. 10x9x8=720

So 60/720=0.083. Is this right for the largest being less than or equal to 5?