how many ways can 3 magazines and 2 newspapers be chosen from 6 magazines and 8 newspapers?
To determine the number of ways to choose 3 magazines and 2 newspapers from the given selection, we can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
Where n represents the total number of items, and r represents the number of items to be chosen. The exclamation point denotes the factorial of a number, which means multiplying that number by all whole numbers smaller than it down to 1.
In this case, we have 6 magazines and 8 newspapers to choose from, and we want to select 3 magazines and 2 newspapers. Using the formula, we can calculate the number of ways to choose them:
Number of ways = (6! / (3!(6-3)!)) * (8! / (2!(8-2)!))
Simplifying this expression, we get:
Number of ways = (6! / (3!3!)) * (8! / (2!6!))
Let's start by calculating the factorial for each number:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
3! = 3 * 2 * 1 = 6
2! = 2 * 1 = 2
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Now substitute these values back into the equation:
Number of ways = (720 / (6*6)) * (40,320 / (2*720))
Simplifying further:
Number of ways = (720 / 36) * (40,320 / 1440)
Number of ways = 20 * 28
Number of ways = 560
Therefore, there are 560 different ways to choose 3 magazines and 2 newspapers from a selection of 6 magazines and 8 newspapers.