How many different groups of 20 can you make from 40?
To find out how many different groups of 20 you can make from 40, you can use a combination formula. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
In this case, n represents the total number of items (40) and r represents the number of items you want to choose (20). The exclamation mark represents the factorial operation, where n! means multiplying all the numbers from 1 to n.
Let's calculate it:
C(40, 20) = 40! / (20!(40-20)!)
First, calculate the factorial of each number:
40! = 40 x 39 x 38 x ... x 3 x 2 x 1
20! = 20 x 19 x 18 x ... x 3 x 2 x 1
Then, calculate the factorial of the difference:
40 - 20 = 20, so (40-20)! = 20!
Now we can substitute the values into the combination formula:
C(40, 20) = 40! / (20!(40-20)!)
= (40 x 39 x 38 x ... x 3 x 2 x 1) / ((20 x 19 x 18 x ... x 3 x 2 x 1) x (20 x 19 x 18 x ... x 3 x 2 x 1))
Now you can simplify the expression algebraically and calculate the value.