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 of 2

(a) In a six-horse field, how many different ways can one make a trifecta bet?

There are

ways to make a trifecta bet.

Part 2 of 2

(b) In a six-horse field, how many different ways can one make a box trifecta bet?

There are

ways to make a box trifecta bet.