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Let X = sum from r=1 to 9 of r * C(9,r)², where C(9,r) denotes the binomial coefficient. Find all values from the list that divide X/1430.
- 9
- 3
- 17
- 19
Correct answer: 9
Solution
Using the identity, X = 9*C(17,8) = 9*24310 = 218790. Then X/1430 = 153 = 9*17. So 9, 3, and 17 divide 153, but 19 does not (153/19 is not integer). Check: 153/9=17, 153/3=51, 153/17=9, 153/19=8.05...
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