Question

Find the number of ways a math test can be made with a 20 question test bank and a 15 question test

Answer 1

Answer: we can make 15,504 different math tests

Explanation:

Ok, we have a bank with 20 questions (Q1, Q2........ , Q20)

and we want to make a test with 15 of those 20 questions.

As the order of the questions does not matter in the thest ( is the same if the order is Q1, Q2, ...., Q15 than if the order is Q15, Q14, ....., Q1 )

So we only want the number of combinations.

When we have N elements and we want to create groups of K elements, the total number of combinations is:

`C = (N!)/((N - K)!*K!)`

Here N = 20 and K = 15

`C = (20!)/(5!*15!) = (20*19*18*17*16)/(5*4*3*2*1) = 15,504`

So we can make 15,504 different math tests