Solutions Problem 8/9, Math 2051, Spring 2002 Problem 34

• 8: 6*6=36
• 9: 3
• 10: 6
• 11: 6+2=8
• 12: 6
• 13: 10
• 14: 11
• 15: 5*5=25
• 16: 2*3*3=18
• 34: 5*5*5=125
• 35: 5*4*3=60
• 36: 5*5=25
• 37: 4*3=12
• 38: 4*4*4=64
• 39: 4*3*2=24
• 40: 5*5*5-4*4*4=61
• 41: 3*4*3=36

Problem 35

• 10: 3!=6
• 11: 3!*3!=36
• 12: 3!=6
• 13: 2*4!=48
• 14: (1/2)*5!=60
• 15: 5!-(4!+4!-3!)=78
• 16: 5!-(2*4!-3!)=78
• 17: C(5,3)*2=20
• 18: 4!+4!-3!=42
• 31: C(13,5)=1287
• 32: C(6,3)C(7,4)=700
• 33: C(13,4)-C(6,4)=700
• 34: C(6,1)C(7,3)+C(7,4)=245
• 35: C(13,4)-[C(6,4)+C(7,4)]=665
• 36: C(13,4)-C(11,2)=660

Problem 36

• 1: 5!=120
• 2: 6!/2!=360
• 3: 12!/(4!2!)=9979200
• 15: C(10+3-1,10)=66
• 16: C(9+3-1,9)=55
• 17: C(4+3-1,4)=15
• 18: C(9+2-1,9)=10
• 19: C(8+2-1,8)=9
• 20: C(10+2-1,10)+C(9+2-1,9)=21
• 21: 4