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

Answer:  

Total 776,520 committees are possible.

Step-by-step explanation:

Since, The total number of students = 20,

The number of students in the committee = 7,

Hence, the possible number of committees can be formed = Total combination of 7 students out of 20 students

$=^{20}C_7$

$=\frac{20!}{7!\times (20-7)!}$

$=\frac{20!}{5040\times 13!}$

$=\frac{20\times 19\times 18\times 17\times 16\times 15\times 14}{5040}$

$=\frac{390700800}{5040}=776520$

⇒ 776,520 committees are possible.