]> Exercise 0.5

Exercise 0.5

Do this and answer the question which is larger, the binomial coefficient C(15,5) or C(14,6)?

Solution:

Strangely enough they are the same.

=-2

=A1+1

=B1+1

=C1+1

=D1+1

=E1+1

=F1+1

=G1+1

=A1+1

1

           

=A2+1

 

=C2+B2

=D2+C2

=E2+D2

=F2+E2

=G2+F2

=H2+G2

=A3+1

 

=C3+B3

=D3+C3

=E3+D3

=F3+E3

=G3+F3

=H3+G3

=A4+1

 

=C4+B4

=D4+C4

=E4+D4

=F4+E4

=G4+F4

=H4+G4

=A5+1

 

=C5+B5

=D5+C5

=E5+D5

=F5+E5

=G5+F5

=H5+G5

=A6+1

 

=C6+B6

=D6+C6

=E6+D6

=F6+E6

=G6+F6

=H6+G6

=A7+1

 

=C7+B7

=D7+C7

=E7+D7

=F7+E7

=G7+F7

=H7+G7

=A8+1

 

=C8+B8

=D8+C8

=E8+D8

=F8+E8

=G8+F8

=H8+G8

=A9+1

 

=C9+B9

=D9+C9

=E9+D9

=F9+E9

=G9+F9

=H9+G9

=A10+1

 

=C10+B10

=D10+C10

=E10+D10

=F10+E10

=G10+F10

=H10+G10

=A11+1

 

=C11+B11

=D11+C11

=E11+D11

=F11+E11

=G11+F11

=H11+G11

=A12+1

 

=C12+B12

=D12+C12

=E12+D12

=F12+E12

=G12+F12

=H12+G12

=A13+1

 

=C13+B13

=D13+C13

=E13+D13

=F13+E13

=G13+F13

=H13+G13

=A14+1

 

=C14+B14

=D14+C14

=E14+D14

=F14+E14

=G14+F14

=H14+G14

=A15+1

 

=C15+B15

=D15+C15

=E15+D15

=F15+E15

=G15+F15

=H15+G15

=A16+1

 

=C16+B16

=D16+C16

=E16+D16

=F16+E16

=G16+F16

=H16+G16

-2

-1

0

1

2

3

4

5

6

7

 

-1

1

                 

0

 

1

0

0

0

0

0

0

0

 

1

 

1

1

0

0

0

0

0

0

 

2

 

1

2

1

0

0

0

0

0

 

3

 

1

3

3

1

0

0

0

0

 

4

 

1

4

6

4

1

0

0

0

 

5

 

1

5

10

10

5

1

0

0

 

6

 

1

6

15

20

15

6

1

0

 

7

 

1

7

21

35

35

21

7

1

 

8

 

1

8

28

56

70

56

28

8

 

9

 

1

9

36

84

126

126

84

36

 

10

 

1

10

45

120

210

252

210

120

 

11

 

1

11

55

165

330

462

462

330

 

12

 

1

12

66

220

495

792

924

792

 

13

 

1

13

78

286

715

1287

1716

1716

 

14

 

1

14

91

364

1001

2002

3003

3432

 

15

 

1

15

105

455

1365

3003

5005

6435

 

16

 

1

16

120

560

1820

4368

8008

11440

 

17

 

1

17

136

680

2380

6188

12376

19448

 

18

 

1

18

153

816

3060

8568

18564

31824

 

19

 

1

19

171

969

3876

11628

27132

50388