1. Suppose we pick the pile of 2 first, the pile of 3 second, and the pile of 6 third. Choose the pile of 2 from the 11 coins in 11C2 = 55 ways Choose the pile of 3 from the remaining 9 coins in 9C3 = 84 ways Choose the pile of 6 from the remaining 6 coins in 6C6 = 1 way. That's (55)(84)(1) = 4620 ways. The answer is 4620. ----------------------------------------- But just for fun, let's suppose we formed the piles in a different order. 2. Suppose we pick the pile of 2 first, the pile of 6 second, and the pile of 3 third. Choose the pile of 2 from the 11 coins in 11C2 = 55 ways Choose the pile of 6 from the remaining 9 coins in 9C6 = 84 ways Choose the pile of 3 from the remaining 3 coins in 3C3 = 1 way. That's (55)(84)(1) = 4620 ways. Or this order: 3. Suppose we pick the pile of 3 first, the pile of 2 second, and the pile of 6 third. Choose the pile of 3 from the 11 coins in 11C3 = 165 ways Choose the pile of 2 from the remaining 8 coins in 8C2 = 28 ways Choose the pile of 6 from the remaining 6 coins in 6C6 = 1 way. That's (165)(28)(1) = 4620 ways. Or this order: 4. Suppose we pick the pile of 3 first, the pile of 6 second, and the pile of 2 third. Choose the pile of 3 from the 11 coins in 11C3 = 165 ways Choose the pile of 6 from the remaining 8 coins in 8C6 = 28 ways Choose the pile of 2 from the remaining 6 coins in 2C2 = 1 way. That's (165)(28)(1) = 4620 ways. Or this order: 5. Suppose we pick the pile of 6 first, the pile of 2 second, and the pile of 3 third. Choose the pile of 6 from the 11 coins in 11C6 = 462 ways Choose the pile of 2 from the remaining 5 coins in 5C2 = 10 ways Choose the pile of 3 from the remaining 3 coins in 3C3 = 1 way. That's (462)(10)(1) = 4620 ways. Or this order: 6. Suppose we pick the pile of 6 first, the pile of 3 second, and the pile of 2 third. Choose the pile of 6 from the 11 coins in 11C6 = 462 ways Choose the pile of 3 from the remaining 5 coins in 5C3 = 10 ways Choose the pile of 2 from the remaining 2 coins in 2C2 = 1 way. That's (462)(10)(1) = 4620 ways. So, as you see, it doesn't matter in which order we pick the 3 piles, the answer is always 4620. In some cases, we have different numbers to multiply, but the answer always comes out to 4620 ways. EdwinM