A recruitment team is required to recruit 9 out of 15 applicant from 3 disciplines,each containing 5 applicants and not required to recruit more than 4 from each disciplines. In how many possible ways can the team make up her choice?
+118608 I invite comment on this one. 
Let me see...
15 applicants. 5 sportA, 5 sportB and 5 sportC
9 will be recruited and not more than 4 from any individual sport
possibilities
441 414 144 I think the number here is 5C4*5C4*5C1 = 3* 5*5*5 = 3*125 = 375
432 423 342 324 234 243 I think the number here is 6*5C4*5C3*5C2 = 6*5*10*10=6*500=3000
333 I think the number here is 1* (5C3)^3 =10^3 = 1000
So there seems to be 10 ways that the numbers from each sport can be chosen.
I think there are 375+3000+1000=4375 different ways that the 9 can be selected. 
+118608 I invite comment on this one.
Let me see...
15 applicants. 5 sportA, 5 sportB and 5 sportC
9 will be recruited and not more than 4 from any individual sport
possibilities
441 414 144 I think the number here is 5C4*5C4*5C1 = 3* 5*5*5 = 3*125 = 375
432 423 342 324 234 243 I think the number here is 6*5C4*5C3*5C2 = 6*5*10*10=6*500=3000
333 I think the number here is 1* (5C3)^3 =10^3 = 1000
So there seems to be 10 ways that the numbers from each sport can be chosen.
I think there are 375+3000+1000=4375 different ways that the 9 can be selected.
