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A local college is forming a seven-member research committee having one administrator, three faculty members, and three students. There are five administrators, 14 faculty members, and 18 students in contention for the committee. How many seven-member committees are possible

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Answer:

1485120

Step-by-step explanation:

Since the order of arrangement does not matter, we use combination :

Recall :

nCr = n! ÷ (n-r)!r!

For administrator : 1 out of 5 :

5C1 = 5! ÷ (5-1)!1!

For faculty members : 3 out of 14 :

14C3 = 14! ÷ (14 - 3)!3!

For students : 3 out of 18 :

18C3 = 18! ÷ (18 - 3)!3!

5C1 * 14C3 * 18C3 = 1485120