Question

You are playing cards and pick up 3 cards. How many different hands are possible if you want at least 1 three?

a) 22,564
b) 16,436
c) 9,876
d) 7,654

Answer 1

To calculate the number of different hands possible with at least one three, we need to consider two cases: when exactly one three is drawn, and when more than one three is drawn. Adding the number of different hands from both cases, we get a total of 20,400. The correct answer is a) 22,564.

Step-by-step explanation:

To calculate the number of different hands possible with at least one three, we need to consider two cases: when exactly one three is drawn, and when more than one three is drawn.

Case 1: Exactly one three is drawn - There are 4 threes in a deck of 52 cards. The remaining 2 cards can be any of the remaining 51 cards. Therefore, the number of different hands with exactly one three is 4 * 51 * 50 = 10,200.

Case 2: More than one three is drawn - There are 4 threes in a deck of 52 cards. The remaining 2 cards can be any of the remaining 51 cards. Therefore, the number of different hands with more than one three is 4 * 51 * 50 = 10,200.

Adding the number of different hands from both cases, we get a total of 10,200 + 10,200 = 20,400 different hands with at least one three. Therefore, the correct answer is a) 22,564.