Hi I need help with this question: A math test has 12 questions. a.) Suppose all

Question

Hi I need help with this question:

A math test has 12 questions.

a.) Suppose all the questions are mulitple choice with 4 answers labeled a, b, c, d. How many ways are there to complete the test

i. If one answer is selected for each question?

ii. If one answer is selected for each question and a, b, c, d are each used at least once?

b.) Suppose the questions are problems instead. In how many way can the total of 100 points be allocated to the 12 problems if each problem counts at least 5 points?

Explanation / Answer

a) i) Since there are 12 questions and each question can be answered in 4 ways the number of ways to complete the test is 412

ii)

The number of ways to complete the test with three options = 312

So the number of ways to complete the test with four options with atleast one option answered = 4*(412-312))

b) Since atleast 5 points have to be given to each of the 12 questions, let us give those points first.

Total points given=12*5=60

So points left =40

Each point can be given to 12 problems.

So the number of ways to distribute the points = 1240

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects