A student is asked to answer 7 out of 13 questions on an exam.
In how many ways can she select the questions to be answered?
That would simply be
C(13,7)
= 13!/(7!6!)
= 1716
To calculate the number of ways a student can select 7 out of 13 questions to be answered, we can use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items (in this case, the total number of questions)
- r is the number of items to be selected (in this case, the number of questions to be answered)
- ! represents factorial, which is the product of all positive integers less than or equal to a given number
In this case, we have n = 13 (total number of questions) and r = 7 (number of questions to be answered).
Using the combination formula:
C(13, 7) = 13! / (7!(13-7)!)
= 13! / (7! * 6!)
Now, let's calculate the value:
13! = 13 * 12 * 11 * 10 * 9 * 8 * 7! (We cancel out 7! since it appears in the denominator)
= 13 * 12 * 11 * 10 * 9 * 8
6! = 6 * 5 * 4 * 3 * 2 * 1
Substituting the values into the formula:
C(13, 7) = (13 * 12 * 11 * 10 * 9 * 8) / (6 * 5 * 4 * 3 * 2 * 1)
Ultimately, C(13, 7) equals 1716.
Therefore, there are 1716 ways in which the student can select 7 out of the 13 questions to be answered.