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8. How many ways can a committee of 5 students be chosen from a student council of 30 students? Is the order in which the members of the committee are chosen important?

User Bart Kiers
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Answer: A committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

No , the order in which the members of the committee are chosen is not important.

Explanation:

Given : The total number of students in the council = 30

The number of students needed to be chosen = 5

The order in which the members of the committee are chosen does not matter.

So we Combinations (If order matters then we use permutations.)

The number of combinations of to select r things of n things =
^nC_r=(n!)/(r!(n-r)!)

So the number of ways a committee of 5 students can be chosen from a student council of 30 students=
^(30)C_5=(30!)/(5!(30-5)!)


=(30*29*28*27*26*25!)/((120)*25!)=142506

Therefore , a committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

User Jeanfrancois
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