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?

Respuesta :

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

[tex]=^{20}C_7[/tex]

[tex]=\frac{20!}{7!\times (20-7)!}[/tex]

[tex]=\frac{20!}{5040\times 13!}[/tex]

[tex]=\frac{20\times 19\times 18\times 17\times 16\times 15\times 14}{5040}[/tex]

[tex]=\frac{390700800}{5040}=776520[/tex]

776,520 committees are possible.

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