roblem 2. Let n be a positive integer. Find the number of permutations a1, a2, ... , An the sequence 1, 2,...,n satisfying a1 < 2a2 < 3az < · < nan. ..

In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1 St place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?

In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (The order of the two letters is not important.)