Question

Miss Morrison has a test bank of multiple choice questions. 15 questions are combinations, and 12 are permutations. Miss Morrison is writing a test with 12 multiple choice questions.

a) How many different tests can she write if she wants to choose 7 combination and 5 permutation multiple choice questions.

b) After she has chosen the 12 questions, in how many orders can she put them on the test?

Answer 1

(a) 5,096,520

(b) 479,001,600

Explanation:

You want to know the number different tests Miss Morrison can write using a question bank of 15 combination questions and 12 permutation questions if her test has 7 combination questions and 5 permutation questions. Further, you want to know the number of ways those 12 questions can be ordered on the test.

(a) Different questions

The number of different tests will be the product of the number of different ways 7 question can be chosen from 15, and the number of ways 5 questions can be chosen from 12:

(15C7)(12C5) = 6435×792 = 5,096,520

where nCk = n!/(k!(n-k)!).

Miss Morrison can write 5,096,520 different tests.

(b) Question order

The first question can be any of the 12 she has chosen. The second question can be any of the remaining 11. This continues until the last question is the only one remaining. The total number of possible test sequences is ...

12·11·10·... ·1 = 12! = 479,001,600

The test can have any of 479,001,600 different question orders.

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