Casey will put 3 plants in a pot. She is picking from 5 different plants in the store. How many possible ways could she pick the plants for the pot?
A10
B20
C40
Please help. Thank you.
5C3 = 5C2 = (5*4)/(1*2) = 10
To calculate the number of possible ways Casey could pick the plants for the pot, we need to use the combination formula. The combination formula is given by:
C(n, r) = n! / ((n - r)! * r!)
Where n is the total number of plants available (5 in this case), and r is the number of plants Casey wants to pick (3 in this case).
Let's calculate now:
C(5, 3) = 5! / ((5 - 3)! * 3!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2!
= 20 / 2
= 10
Therefore, there are 10 possible ways Casey could pick the plants for the pot.
So the answer is A) 10.
To determine the number of possible ways Casey can pick the plants for the pot, we can use the concept of combinations.
In this scenario, Casey wants to pick 3 plants out of the 5 different plants available in the store. The order in which she selects the plants does not matter, since all three plants will end up in the same pot.
The formula for calculating combinations is given by:
nCr = n! / (r! * (n-r)!)
where n is the total number of items to choose from, and r represents the number of items to be chosen.
Using this formula, we can calculate the number of possible ways Casey can pick the plants:
5C3 = 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2)
= 5 * 4 / 2
= 10
Hence, Casey could pick the plants for the pot in 10 possible ways, which is option A.