Question

A TEACHER IS CONSTRUCTING A MATHEMATICS TEST

Answer 1

The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

How to determine the combination

Note that the formula for combination is given as;

Combination = $\frac{n!}{r!(n-r)!}$

From the information we have that;

There are 28 questions in the pool

The test should have a total of 10 questions;

6 difficult , 10 average and 12 easy questions

We are asked to determine the combination of;

3 difficult questions

4 average questions

3 easy questions

6C3 = $\frac{6!}{3!(6-3)!}$

6C3 = $\frac{720}{36}$

6C3 = 20

10C4 = $\frac{10!}{4!(10-4)!}$

10C4 = $\frac{3628800}{17280}$

10C4 = 210

12C4 = $\frac{12!}{4!(12-4)!}$

12C4 = 220

The number of ways of constructing the questions is

= 20 × 210 × 220

= 924, 000 ways

Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

Learn more about combination here:

brainly.com/question/4658834

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