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0006

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  • 1. Today’s Math Question 2009 11 16 0006 (x + y + z)8 xy 2z 5 x,y,z
  • 2. Today’s Math Answer 0006 ( ) (x + y + z)8 xa y b z c ( )( ) a + b + c = 8, a 1, b 1, c 1 a + b + c = 8, a 0, b 0, c 0 ↔ a + b + c = 5, a 0, b 0, c 0 a, b, c a, b, c 8 10! 7! 8+2 C2 = = 45 . . . . . . 5+2 C2 = = 21 . . . . . . 8!2! 5!2!
  • 3. ( ) (x + y + z)8 x = 1, y = 1, z = 1 (1 + 1 + 1)8 = 38 x, y, z x8 , y 8 , z 8 3 x, y, z xa y b (a + b = 8, a 1, b 1) x = 1, y = 1 (1 + 1)8 = 28 x8 , y 8 28 − 2 y b z c , xa z c 3 × (28 − 2) 38 − 3 − 3 × (28 − 2) = 5796 . . . . . .