katie is going to adopt kittens from a litter of 11. how many ways can she choose a group of 3 kittens?
To find the number of ways Katie can choose a group of 3 kittens from a litter of 11, we can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of objects, and r is the number of objects to be chosen.
In this case, n = 11 (total number of kittens) and r = 3 (number of kittens to be chosen).
Using the formula, the number of ways Katie can choose a group of 3 kittens is:
C(11, 3) = 11! / (3! * (11 - 3)!) = 11! / (3! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165
Therefore, Katie can choose a group of 3 kittens from a litter of 11 in 165 different ways.
To determine the number of ways Katie can choose a group of 3 kittens from a litter of 11, we can use the concept of combinations. The formula for combinations is nCr, where n is the total number of objects and r is the number of objects being chosen without regard to their order.
In this case, Katie wants to choose 3 kittens from a litter of 11. So, we can calculate it using the formula:
nCr = n! / (r! * (n-r)!)
where "!" represents the factorial operation.
Applying this formula, we can calculate the number of ways Katie can choose 3 kittens:
11C3 = 11! / (3! * (11-3)!)
Now, let's break down the calculation:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
3! = 3 x 2 x 1
(11-3)! = 8!
Substituting these values into the formula, we get:
11C3 = (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((3 x 2 x 1) * (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1))
Simplifying the expression further:
11C3 = (11 x 10 x 9) / (3 x 2 x 1)
11C3 = 165
Therefore, Katie can choose a group of 3 kittens from a litter of 11 in 165 different ways.