Suppose i have a deck of 40 cards numbered 1-10 in red, yellow, blue, and green. suppose i am dealt 5 cards. how may cards could be dealt first?
40-5= 35
To determine how many cards could be dealt first, you need to calculate the number of possible combinations when selecting 5 cards from a deck of 40 cards.
Since the order in which the cards are dealt does not matter, you need to calculate the number of combinations, which is given by the formula:
C(n, r) = n! / (r!(n-r)!)
Where:
- n represents the total number of cards in the deck (40 in this case),
- r represents the number of cards you want to select (5 in this case),
- ! represents the factorial operation (the product of all positive integers up to the given number).
Using this formula, you can calculate the number of different combinations:
C(40, 5) = 40! / (5!(40-5)!)
Simplifying the equation further:
C(40, 5) = 40! / (5!35!)
Now, you can calculate the value:
40! = 40 x 39 x 38 x 37 x 36 x ... x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
35! = 35 x 34 x 33 x 32 x ... x 3 x 2 x 1
Plugging these values into the formula:
C(40, 5) = (40 x 39 x 38 x 37 x 36 x ... x 3 x 2 x 1) / [(5 x 4 x 3 x 2 x 1) x (35 x 34 x 33 x 32 x ... x 3 x 2 x 1)]
After calculating this, the result is:
C(40, 5) = 658,008
Therefore, there are 658,008 different ways you can be dealt the first 5 cards out of the 40-card deck.