Mary purchased a package of 13 different plants, but she only needed 9 plants for planting. In how many ways can she select the 9 plants from the package to be planted?
This would be an example of the C(n,r) that I explained in a few posts below.
You are choosing 9 from the 13, and the order really does not matter, so
C(13,9) = 13!/(9!4!) = 715
look for a key labeled nCr on your calculator
press
13
2ndF
nCr
9
=
you should get 715
yea i was having a problem because the calculator i have doesnt have the F button, but thanks for helping me...it was very confusing to me...
To find the number of ways Mary can select 9 plants from the package of 13 plants, you can use the concept of combinations.
The number of ways to select a subset of 9 plants from a package of 13 plants can be calculated using the formula for combinations, which is denoted as C(n, r) or "n choose r." In this case, n represents the total number of plants (13) and r represents the number of plants to be selected (9).
The formula for combinations is: C(n, r) = n! / (r! * (n - r)!)
Here, "!" denotes the factorial of a number, which means multiplying all positive whole numbers from that number down to 1.
Applying this formula, the number of ways Mary can select 9 plants from the package of 13 plants is:
C(13, 9) = 13! / (9! * (13 - 9)!)
To simplify this expression, calculate the factorial of each number involved:
13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
(13 - 9)! = 4! = 4 * 3 * 2 * 1
Now substitute these values into the original formula:
C(13, 9) = 13! / (9! * 4!)
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) * (4 * 3 * 2 * 1))
By simplifying the expression further, you can cancel out some terms:
C(13, 9) = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
= 715
Therefore, Mary can select the 9 plants from the package in 715 different ways.