How many ways can Grant arrange 3 of his 10 plants on a window ledge?
The number of ways to arrange 3 plants out of 10 is given by the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of plants (10), and r is the number of plants to be arranged (3).
Plugging in the values, we get:
10C3 = 10! / (3!(10-3)!)
= 10! / (3!7!)
= (10 * 9 * 8 * 7!) / (3! * 7!)
= (10 * 9 * 8) / (3 * 2)
= 10 * 3 * 4
= 120
Therefore, there are 120 ways that Grant can arrange 3 of his 10 plants on the window ledge.
To find the number of ways Grant can arrange 3 of his 10 plants on a window ledge, we can use the concept of combinations.
The number of ways to choose 3 plants out of 10 can be found using the formula for combinations:
C(n,r) = n! / (r! * (n-r)!)
where n is the total number of plants and r is the number of plants to be chosen.
In this case, Grant has 10 plants and he wants to choose 3 of them, so n = 10 and r = 3.
Plugging these values into the formula, we get:
C(10,3) = 10! / (3! * (10-3)!)
C(10,3) = 10! / (3! * 7!)
Now, we can simplify the expression:
10! = 10 * 9 * 8 * 7!
C(10,3) = (10 * 9 * 8 * 7!) / (3! * 7!)
Since 3! * 7! = (3 * 2 * 1) * 7!, the 7! term cancels out, and we are left with:
C(10,3) = 10 * 9 * 8 / (3 * 2 * 1)
Simplifying further, we get:
C(10,3) = 10 * 3 * 4 = 120
Therefore, there are 120 ways Grant can arrange 3 of his 10 plants on a window ledge.