if you have a standard deck of 52 cards, in how many different ways can you deal out.
a) 4 queens
There are 4! ways to deal out 4 queens.
Now, the chance of actually dealing 4 queens is
4/52 * 3/51 * 2/50 * 1/49 = 4!/(52! / 48!) = (4!48!)/52! = 1/270725
Is that the only answer choice or?
It was a question. The textbook stated: if you have a standard deck of 52 cards, in how many different ways can you deal out. and the textbook was asking to find 4 queens in the deck how many possibilities. so the four queens was a sub question to the main question.
To find out how many different ways you can deal out 4 queens from a standard deck of 52 cards, we can use the concept of combinations.
First, we need to determine the total number of ways you can choose 4 cards from a set of 52 cards, which can be calculated using the formula for combinations, denoted as "nCr" or "C(n,r)":
nCr = n! / (r! * (n-r)!)
For this case, since we're selecting 4 cards from a set of 52 cards, the calculation becomes:
C(52, 4) = 52! / (4! * (52-4)!)
Now, let's calculate the value:
C(52, 4) = 52! / (4! * 48!)
To simplify the calculation, we can use the factorials:
52! = 52 * 51 * 50 * ... * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
48! = 48 * 47 * 46 * ... * 3 * 2 * 1
Now let's calculate:
C(52, 4) = (52 * 51 * 50 * 49 * 48!) / (4! * 48!)
A lot of factors in the numerator and denominator will cancel out, leaving us with:
C(52, 4) = (52 * 51 * 50 * 49) / (4 * 3 * 2 * 1)
After simplifying the expression, we find that:
C(52, 4) = 270,725
Therefore, there are 270,725 different ways to deal out 4 queens from a standard deck of 52 cards.