Twenty girls are trying out for the cheer squad. How many different 12 girl teams can be made
combinations of 20 taken 12 at a time
= 20! / [ 12! (8!) ]
= 125,970 ( I looked it up in a table of binomial coefficients )
To find out the number of different 12-girl teams that can be made from a group of 20 girls, we can use the concept of combinations.
In this case, we need to select 12 girls out of the 20 available. The order in which the girls are selected does not matter, as long as we end up with a team of 12 girls. This is known as a combination.
The formula for finding the number of combinations is given by:
nCr = n! / (r!(n-r)!)
Where:
- n is the total number of objects (in this case, 20)
- r is the number of objects we want to select (in this case, 12)
- ! denotes the factorial of a number (the product of all positive integers less than or equal to the number)
Plugging in the values into the formula, we get:
20C12 = 20! / (12!(20-12)!)
Simplifying further:
20C12 = 20! / (12! * 8!)
To calculate this value, we can use a calculator or a mathematics software that can handle factorials. The result will be the number of different 12-girl teams that can be formed from the group of 20 girls.