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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.
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=-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
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=D13+C13
|
=E13+D13
|
=F13+E13
|
=G13+F13
|
=H13+G13
|
|
=A14+1
|
|
=C14+B14
|
=D14+C14
|
=E14+D14
|
=F14+E14
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=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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