Question

A college professor hands out a list of 10 questions, 5 of which will appear on the final exam for the course. One of the students taking the course is pressed for time and can prepare for MATH 270 Assignment 2 W. Li 2 only 7 of the 10 questions on the list. Suppose the professor chooses the 5 questions at random from the 10. a) What is the probability that the student will be prepared for all 5 questions that appear on the final examination

Answer 1

21 / 252

Explanation:

Recall : nCr = n! ÷ (n-r)!r!

The total possible outcome ; 5 questions out of 10

10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252

Required outcome :

All 5 questions set being from the 7 questions covered and 0 from the 3 left uncovered

7C5 * 3C0

7C5 = 7! ÷ 2!5! = (7*6) ÷ (2*1) = 21

3C0 = 3! ÷ 3!0! = 1

Probability = required outcome / Total possible outcomes

P(All 5 questions prepared for appears) :

[7C5 * 3C0] ÷ 10C5

(21 * 1) / 252

= 21 / 252