Asked Dec 22, 2019

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?


Expert Answer

Step 1


         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

Step 2


         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

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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