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?

Probability that they are the youngest is 0.000549

Step-by-step 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)