SOLUTIONS TO PREVIOUS TESTS
1. (8pt) Test A: C(5+13-1,13) - 5*C(5+7-1,7) + C(5,2)*C(5+1-1,1); Test B: C(5+12-1,12) - 5*C(5+7-1,7) + C(5,2)*C(5+2-1,2);
2. (8pt) Test A a) e1 + e2 + . . +e6 = 31, ei>=2, b) (x^2 + x^3 + . . )^6, coef.of x^31, c) C(6+19-1,19);
Test B: a) e1 + e2 + . . . + e7 = 29, ei>=2, b) (x^2 + x^3 + . .)^7, coef. of x^29, c) C(7+15-1,15).
3. (8pt) Test A: C(13,1)C(4,4)C(12,2)C(4,1)^2/C(52,6); Test B: C(6,2)C(4,1)24^3.
4. (8pt) Test A: C(5,2)C(3,1)24^2; Test B: C(13,1)C(4,3)C(12,2)C(4,1)^2/C(52,5).
5. (8pt) Both Tests: C(3,2)*7!/2!.
6. (14pt) Test A: C(5+(6-4)-1,(6-4))*4!/2!*(6!/2!-1); Test B: C(6+(7-5)-1,(7-5)*(5!/2!2! - 1)*7!/2!.
7. (12pt) First pick subset of positions where A's and B's will go; put an A in the first of these positions and then distribute the remaining A's and B's in the other positions; Test A: C(16,11)*10!/4!6!; Test B: C(17,12)*11!/3!8!.

Solution to Fall 2006 301 Test 2
1. C(7+18-1,18) - 7C(7+9-1,9) + C(7,2)*1.
2. e1 + e2 + . . e6 = 29, 4 =< ei; (x^4 + x^5 + . . .)^6, coef x^29; C(6+5-1,5)
3. 5!*21!
4. C(13,3)C(4,2)^3*40
5. 3(8!/3!3!2! + 8!/4!2!2!)
6. C(4+(8-3)-1,(8-3))*1*4!/2!
7. 4*C(4+(11-5)-1,(11-5))-C(4,2)C(4+(11-10)-1,(11-10)).

Solutions to Fall 2005 301 Test 2
1. C(5+10-1,10) - 5*C(5+6-1,6) + C(5,2)C(5+2-1,2);
2. a) e1 + .. +e8 = 25, ei>=2, b) (x^2 + . .. )^8, x^25, c) C(8+9-1,9);
3. C(13,4)*4^4/C(52,4).
4. C(6,r)*9^(6-r).
5. 11!/(3!2!)-10!/(2!2!).
6. C(4+(7-6)-1,(7-6))*1*4!/(2!2!).
7. sum k=0 to 4 of C(3+k-1,k)C(4+(9-2k)-1,(9-2k)),