Mrs A wants to produce a different sets of test questions for her essay test. If she plans to do this by putting together 3 out 5 questions she prepared, how many different sets of questions could she construct?
To find the number of different sets of questions Mrs A could construct, we can use the combination formula.
The formula for combinations is:
nCr = n! / [r!(n-r)!]
Where:
n = total number of questions (5 in this case)
r = number of questions chosen (3 in this case)
Substitute the values into the formula:
5C3 = 5! / [3!(5-3)!]
5C3 = 5! / [3!2!]
Calculate the factorials:
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
2! = 2 x 1 = 2
Substitute the factorial values back into the formula:
5C3 = 120 / (6 x 2)
5C3 = 120 / 12
5C3 = 10
Therefore, Mrs A could construct 10 different sets of questions by putting together 3 out of the 5 questions she prepared for her essay test.