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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 |
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