Question #f07f8

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Question #f07f8

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Answer 1 · 2017-08-03T07:45:54

$(30!)/(6!(30-6)! ) = 593,775$

Explanation:

$20%$ of the students will be evaluated. The order in which the teacher sees them is not important, as long as $6$ of them are chosen.

There are $30$ choices for the first student, then $29$ for the second, then $28$ and so on until $6$ students are chosen.

The total number of possible groups of $6$ is

$30xx29xx28xx27xx26xx25$

This can also be written as $(30!)/((30-6)!)$

$(30*29*28*27*26*25cancel(*24*23*22 ...).)/cancel(24*23*22*...)$

However within this number of groups, the same groups just in a different order are included, so we need to reduce the number by the number of ways of arranging $6$ students which is $6!$

The number of different groups of $6$ students is:

$(30!)/(6!(30-6)! ) = 593,775$

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