Katie is going to adopt kittens from a litter of 11. How many ways can she choose a group of 3 kittens?
that's just "11 choose 3" or C(11,3) or
11!/(3!8!) = 165
i THiNk itS 33 :)
<33
Maria, I am 100% sure I am right.
How sure are you?
To calculate the number of ways Katie can choose a group of 3 kittens from a litter of 11, we can use the combination formula. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items to choose from (in this case, the litter of 11 kittens)
- r is the number of items we want to choose (in this case, a group of 3 kittens)
- ! denotes the factorial operation (multiplying a number by all positive whole numbers less than itself)
Using this formula:
C(11, 3) = 11! / (3!(11-3)!)
Simplifying the equation:
C(11, 3) = 11! / (3!8!)
Calculating the factorial values:
C(11, 3) = (11 * 10 * 9 * 8!) / (3 * 2 * 1 * 8!)
Canceling out the 8! terms:
C(11, 3) = (11 * 10 * 9) / (3 * 2 * 1)
Performing the multiplication:
C(11, 3) = 990 / 6
Simplifying the fraction:
C(11, 3) = 165
Therefore, there are 165 different ways Katie can choose a group of 3 kittens from the litter of 11.