Mathematics 2013 JAMB Past Questions - Question 48: In how many ways can three seats be occupied if 5 people are willing to sit?

Correct Answer

C

Explanation

5 people can take 3 places in 3P3 ways, = 5! /(5-3)! = 5! /2!= 5 x 4 x 3 x 2! / 2!= 5 x 4 3 = 60waysTo determine the number of ways three seats can be occupied by five people, we can use the concept of permutations.The number of ways to arrange 'r' objects from a set of 'n' objects is given by the formula for permutations, which is denoted as P(n, r) and calculated as:P(n, r) = n! / (n-r)!In this case, we have 'n' as 5 (number of people) and 'r' as 3 (number of seats to be occupied).Plugging these values into the formula, we get:P(5, 3) = 5! / (5-3)!Calculating the factorial terms:5! = 5 * 4 * 3 * 2 * 1 = 120(5-3)! = 2! = 2 * 1 = 2Substituting these values into the formula:P(5, 3) = 120 / 2 = 60Therefore, there are 60 ways for three seats to be occupied by five people.