of the 2598960 different 5 card hands possible from a deck of 52 playing cards, how many would contain all 4 tens?
If you hold 4 tens in your hands, how many cards are left for the fifth card?
48
Right!
To determine the number of 5-card hands that contain all four tens, we need to consider the following:
1. The number of ways to choose the four tens from the deck: There are 4 tens in a standard deck, so we have to choose all four of them. This can be calculated using the combination formula, C(n, k), where n is the total number of elements (4 tens) and k is the number of elements we want to choose (4). Therefore, C(4, 4) = 1.
2. The number of ways to choose the remaining card (not a ten) from the remaining 48 cards in the deck: Since we have already chosen all four tens, we need to choose one more card from the remaining 48 cards in the deck. This can be calculated using the combination formula as well, C(48, 1) = 48.
To find the number of 5-card hands containing all four tens, we multiply the results of the two steps:
1 * 48 = 48.
Therefore, there are 48 different 5-card hands possible that contain all four tens.