the game of the euchre uses just 9s,10s,jacks,queens,kings and aces from a standard deck of 52 cards. how many five-card euchre hands have all black cards.
is the right answer 495 ways
which i got by doing 12C5 x 40C0
= 495 ways
How did you get 495 from 12C5
12C5 = 792 and of course 40C0 = 1
so it should be 792
To find the number of five-card euchre hands that have all black cards, we need to break down the problem step by step.
Step 1: Calculate the number of ways to select 5 cards from a deck containing only 9s, 10s, jacks, queens, kings, and aces. This is represented by the term 12C5, which indicates the combination of selecting 5 items from a pool of 12 items. Therefore, 12C5 equals 792.
Step 2: Calculate the number of ways to select 0 black cards from the remaining 40 cards in the deck. This is referred to as 40C0, since you are choosing 0 black cards from a pool of 40 black and red cards. Choosing 0 from any pool of items equals 1, so 40C0 is also equal to 1.
Step 3: Multiply the results from Steps 1 and 2 together. 792 x 1 equals 792.
Therefore, based on the calculations provided, there are 792 different ways to get a five-card euchre hand that consists of all black cards. It seems that the answer of 495 is incorrect and may be the result of a miscalculation or misunderstanding of the problem.