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- 1- 49 50 = 100(X)
- 2- 49 50 > 100(O) => C(2,2) = 1x2 / 1x2
- 3- 48 49 50 => C(3,2) = 2x3 / 1x2
- 4- 47 48 49 50 => C(4,2) = 3x4 / 1x2
- 5- 46 47 48 49 50 => C(5,2) = 4x5 / 1x2
- ....
- 24- 27 28 ... 50 => C(24,2) = 23x24 / 1x2
- ------------------------------
- 25 26 27 ... 50 => C(26,3) = 24x25x26 / 1x2x3 = 2600
- -------------------------------
- 全加起來
- => 1x2 + 2x3 + 3x4 + 4x5 + ... + 23x24 / 1x2 + 2600
- -------------------------------------------------------------------
- 套公式 [ 1x2 + 2x3 + ... + nx(n+1)= n(n+1)(n+2)/3 ]
- n=23
- => 23x24x25 / 3 = 4600
- --------------------------------------------------------------------
- => 4600 / 1x2 +2600 = 4900
- => 分子 =4900
- 分母=C(50,3)=19600
- = 1/4
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