Third Test Solutions

Solution to Fall 20010 Third Test
1. (8 pt) Test A: 5! - 9x4! + 26x3! - 26x2! + 8x1!; Test B: 5! b 9x4! + 27! b 31x2! + 12x1!
2. (8 pt) Test A: 3^10 b 3x2^10 + 3; Test B: 3^12 b 3x2^12 + 3.
3. (4 pt) Test A: an,k = an-2,k-1 + an-5,k-1 + an-8,k-1; Test B: an,k = an-2,k-1 + an-3,k-1 + an-4,k-1 + an-5,k-1.
4. Test A: a) (5 pt) an = 2an-1 + 2an-2, b) (5 pt) an = 3an-1 - an-3 Test B: parts a) and b) reversed.
5. (14 pt) Test A: P(C(8,2),5) - 8xP(C(7,2),5) + C(8,2)xP(C(6,2),5) - C(8,3)xP(C(5,2),5) + C(8,4)xP(C(4,2),5);
Test B: P(C(9,2),8) - 9xP(C(8,2),8) + C(9,2)xP(C(7,2),8) - C(9,3)xP(C(6,2),8) + C(9,4)xP(C(5,2),8).

Solution to Fall 2009 Third Test
1. 5! - 8x4! + 21x3! - 20x2! + 6x1!
2. 10!/3!3!2! -(2x8!/2!3! + 9!/3!3!) + (2x7!/3! + 6!/2!) - 5!
3. an,k = an-3,k-1 + an-5,k-1 + an-8,k-1.
4. a) an = an-2 + an-3 + an-4, b) an = an-2 + an-3 + an-4 - an-6.
5. C(P(8,3),30) - 8xC(P(7,3),30) + C(8,2)xC(P(6,3),30) - C(8,3)xC(P(5,3),30).

Solution to Fall 2008 Third Test
1.5! - 8x4! + 21x3! - 20x2! + 6x1! .
2. C(37,12)- [C(22,12) + C(25,12) + C(27,12)} + C(15,12) + C(12,12).
3. an,k = an-2,k-1 + an-3,k-1 + an-4,k-1 + an-5,k-1.
4. a) an = an-1 + an-2 + an-3, b) an = an-1 + an-2 + an-3 - an-6.
5. 35^10 - 5*34^10 + C(5,2)*33^10 - C(5,3)*32*10 + C(5,4)*31^10 - 30^10.