Finite Math Question

Answer:
12!/(6! * 3! * 3!)
= 479001600/(720 * 6 * 6)
= 18480

Explanation 1:
Out of 12 newly hired telemarketers, choose 6 from them to be assigned to the Survey division.
The number is 12C6.
In the remaining 12 - 6 = 6 officers, choose 3 from them to be assigned to the Fundraising division.
The number is 6C3.
For the final remaining 6 - 3 = 3 officers, choose all 3 to be assigned to the Direct Sales division.
The number is 3C3.
The total number of ways is
12C6 * 6C3 * 3C3
= 12!/(6! * 6!) * 6!/(3! * 3!) * 3!/(3! * 0!)
= 12!/(6! * 3! * 3!)

Explanation 2:
Consider the permutation of 12 newly hired telemarketers in a row.
There are 12! of ways.
Assign the first 6 to the Survey division, the next 3 to the Fundraising division, the last 3 to the Direct Sales division.
Then, the arrangements within the first 6 do not affect the overall assignment, thus the above number needs to be divided by 6!.
Similarly, for the middle 3 and the final 3, the total number needs to be divided by 3! for each of the two groups.
Thus, the total number of ways is
= 12!/(6! * 3! * 3!)