Question

1. a class has 8 students who are to be assigned seating by lot. what is the probability that the students will be arranged in order from shortest to tallest? (assume that no two students are the same height.) a) 0.1000 b) 0.00019841 c) 0.00024802 d) 0.0000248

Explanation:

Step1: Calculate total arrangements

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 8\), so the total number of ways to arrange 8 students is \(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1=40320\).

Step2: Determine favorable arrangements

There is only 1 way to arrange the 8 students from shortest to tallest.

Step3: Calculate probability

The probability \(P\) of an event is the number of favorable outcomes divided by the number of total outcomes. So \(P=\frac{1}{8!}=\frac{1}{40320}\approx0.0000248\).

Answer:

D. 0.0000248