52. In a box, there are 12 balls, identical in every way, except that they are numbered 1 through 12.We draw 6 balls at random and without replacement one by one.What is the probability that the numbers on the balls appear in increasing order but not necessarily consecutive?

Hint: There is a one-to-one correspondence between all the possible ways that the numbers on the balls drawn are in increasing order and the set of subsets of

{1, 2, . . . , 12} with exactly 6 elements.