Question

Playing the horses: In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order. Part 1 out of 2 In a seven-horse field, how many different ways can one make a trifecta bet? There are ways to make a trifecta bet.

Answer 1

In a trifecta bet, one needs to tell the first 3 horses and the correct order also.

So in a 7 horse field, number of different ways one can make a trifecta bet = 7*6*5 = 210

Hence there are 210 different ways to make a trifecta bet.

And although not asked in the question, number of different ways to make a box trifecta bet = 210/(3!) = 210/6 = 35