A professor will assign seven projects to three students. If two students each got 2 projects, and the other one got 3 projects, how many ways are possible?  Choose the correct choice.
A) 600
B) 630
C) 650
D) 670
E) 690
The projects are all distinct and so are the students. So in both the cases, you are doing essentially the same. In the first case, you are assigning 7 things to 3 people and in the second case, you are assigning 7 people to 3 things.   So in both the cases, you choose the person/thing that will get 3 things/person in 3C1 = 3 ways.   Next, you choose 3 things/people out of 7 in 7C3 ways.   Next, you choose 2 things/people out of the remaining 4 in 4C2 ways.   3C1 * 7C3 * 4C2 = 3*(7*6*5)/(3*2) * 6= 
<gadget id="calculator">3*(7*6*5)/(3*2) * 6</gadget>
<output>630</output>
630 ways	ANS:630
<result>B</result>
A professor will assign seven projects to three students. If two students each got 2 projects, and the other one got 3 projects, how many ways are possible?