Question

There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selecting 7 students from student council. How many possible committees can be formed?

Answer 1

Since the students are to be selected at random, the concept used is Combination. The combination is 20C7 which means that "combination of 20 taken 7". The numerical value of the combination is 77520. Thus, there are 77520 ways of choosing the members of the student council. 

Answer 2

There are 77520 ways of choosing the members of the student council.

What is a combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

Since the students are to be selected at random, the concept used is Combination. The combination is 20C7. which means that "combination of 20 taken 7".

$^{20}C_7=\dfrac{20!}{7!(13!)}$

$^{20}C_7=77520$

The numerical value of the combination is 77520. Thus, there are 77520 ways of choosing the members of the student council.

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