Please help! This is a Combinations problem.

In a standard deck of cards, how many 4-card hands are there that contain at most 1 heart?

I keep getting 118,807 but the real answer is suppose to be 201, 058. I always get confused with card questions. Can you help me?

Question

Please help! This is a Combinations problem.

In a standard deck of cards, how many 4-card hands are there that contain at most 1 heart?

I keep getting 118,807 but the real answer is suppose to be 201, 058. I always get confused with card questions. Can you help me?

anonymous · Answer

You can choose one heart in 13 ways and for each of these you can choose 3 non-hearts in $$^{39}C_{3}$$ ways. You can choose 4 non-hearts in $$^{39}C_{4}$$. So the answer is $$13 * ^{39}C_{3} + ^{39}C_{4}$$