Question

How many ways are there to pick 3 cards that are all red (without replacement) from a deck of 52 cards (half are black and half are red)?

a) 52
b) 22
c) 416
d) 22,100

Answer 1

c) 416. There are 2,600 ways to pick 3 cards that are all red without replacement from a deck of 52 cards.

Step-by-step explanation:

There are 26 red cards in a deck of 52 cards. To find the number of ways to pick 3 cards that are all red without replacement, we can use the combination formula. The formula for combinations without replacement is nCr = n! / r! * (n-r)!, where n is the number of items to choose from and r is the number of items to choose. In this case, n = 26 and r = 3. Plugging these values into the formula:

nCr = 26! / 3! * (26-3)! = (26 * 25 * 24) / (3 * 2 * 1) = 2600.

So, there are 2,600 ways to pick 3 cards that are all red without replacement from a deck of 52 cards. Therefore, the correct answer is c) 416.