Did you know?
Did you know that you can use the nCr formula to solve the problem of how many different directions can be chosen for the push buttons in Jamie's restaurant?
The nCr formula, also known as the combination formula, is used to calculate the number of ways to choose a certain number of items from a larger set without regard to the order in which they are arranged.
In this case, we have four push buttons on each claw machine and seven identical machines. To find the total number of different directions that can be chosen for the push buttons, we can use the nCr formula.
Step 1: Define the variables:
Let n be the total number of items (buttons)
Let r be the number of items to be chosen from the total (directions)
Step 2: Apply the formula:
The nCr formula states nCr = n! / (r! * (n-r)!), where "!" represents the factorial function.
In this scenario, we have n = 4 (the total number of buttons) and r = 4 (since we want to choose all buttons).
Step 3: Calculate the factorials:
Calculate the factorials of n, r, and (n-r).
n! = 4! = 4 * 3 * 2 * 1 = 24
r! = 4! = 24
(n-r)! = (4-4)! = 0! = 1
Step 4: Plug the values into the formula:
nCr = 24 / (24 * 1) = 24
Therefore, there are 24 different directions that can be chosen for the push buttons on each claw machine in Jamie's restaurant.
