MATHEMATICS

JAMB 2009 - Question 48

Mathematics 2009 JAMB Past Questions - Question 48: In how many ways can 9 people be seated if 3 chairs are available?

In how many ways can 9 people be seated if 3 chairs are available?
A:
B:
C:
D:
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Correct Answer

B

Explanation

n! /n-r! = 9! /9-3! = 9! /6! = 9x8x7=504If there are 9 people and 3 chairs available, we can determine the number of ways they can be seated using the concept of permutations.Since the order of seating matters, we can use the formula for permutations:P(n, r) = n! / (n - r)!where n is the total number of people and r is the number of available chairs.In this case, we have 9 people (n = 9) and 3 chairs (r = 3). Plugging these values into the formula:P(9, 3) = 9! / (9 - 3)!        = 9! / 6!Calculating the factorials:9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 16! = 6 * 5 * 4 * 3 * 2 * 1Simplifying the expression:P(9, 3) = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1)        = 9 * 8 * 7        = 504Therefore, there are 504 ways in which the 9 people can be seated if 3 chairs are available.