For a calculus quiz, the teacher will choose 11 questions from the 15 in a set of review exercises. How many different sets of questions could the teacher choose
you should be familiar with the "choose" notation.
What is C(15,11) ?
To find the number of different sets of questions the teacher could choose, we need to use the concept of combinations.
In this problem, we need to choose a subset of 11 questions from a set of 15. The order in which the questions are chosen does not matter.
The formula for the number of combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items to choose from (in this case, 15 questions),
- r is the number of items to choose (in this case, 11 questions),
- n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
Plugging the values into the formula, we get:
C(15, 11) = 15! / (11!(15-11)!)
= 15! / (11! * 4!)
Calculating the factorials:
15! = 15 * 14 * 13 * 12 * 11!
4! = 4 * 3 * 2 * 1
Substituting these values, we have:
C(15, 11) = (15 * 14 * 13 * 12 * 11!) / (11! * 4 * 3 * 2 * 1)
Simplifying the equation:
C(15, 11) = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
= 27,720
Therefore, the teacher could choose from 27,720 different sets of questions.