Question
Asked Dec 22, 2019
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In Exercises 5–36, express all probabilities as fractions.

Sorting Hat 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?

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Expert Answer

Step 1

Permutation:

         The act of arranging the members of a set into an order or sequence, if it is already in order, we want to rearrange its elements.

The formula for computing permutation is

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n! „P": (n-r)! where nis the mumber of elements in a set r is the number of arranged elements to calculate

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Step 2

Combination:

         A combination is a selection of all object or part of a set of objects, without regard to the order in which objects are selected.

The formula for computing combination is

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n! „C' =(",)=; r!(n-r)! where nis the number of elements in a set r is the mmber of arranged elements tocalculate

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Step 3

Given that,

Selecting 4 students from 16 students

Here in the process of selecting, ...

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n =16 16! 16 C, = 4!(16 – 4)! 16! 4!(12)! 16x15x14x13×12! 4x 3x2x1(12!) 16x15x14x13 4x 3 x 2x1 =1820

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