Question

At Hogwarts School of Witchcraft and Wizardry, the Sorting Hat chooses one of four houses for each first-year student. If 4 students are randomly selected from 16 available students (including Harry Potter), what is the probability that they are the four youngest students?

Answer 1

Probability that they are the youngest is 0.000549

Explanation:

Given

Number of students = 16

Selected students = 4

Let n = number of students

n = 16

Let r = selections

r = 4

We're interested in selecting 4 students out of 16; the keyword, selection means we're dealing with combination because order is not important.

So,

Solving for nCr

nCr = n!/((n-r)!r!)

16C4 = 16!/((16-4)!4!)

16C4 = 16!/(12!4!)

16C4 = 16 * 15 * 14 * 13 * 12!/(12!4!)

16C4 = 16 * 15 * 14 * 13 / 4 * 3 * 2 * 1

16C4 = 1820 ways

There are 1820 ways of selecting 4 students from a total of 1820.

Only one of these ways can the four of them be the youngest.

So, probability = 1/1820

Probability = 0.0005494506

Probability that they are the youngest is 0.000549 (approximately)