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The value ofsum_(r=0)^(10) (-1)^(r).4^(10-r)""^(30)C_(r)""^(30-r)C_(10-r) is equal to |
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Answer» `.^(30)C_(10) xx 2^(10)` ` = underset(r=0)overset(10)sum(-1)^(r)..4^(10-r).(30!)/((30-r)!r!) .((30-r)!)/(20!(10-r)!)` `= (30!)/(20!)underset(r=0)overset(10)sum(-1)^(r).4^(10-r).(1)/(r!(10-r)!)` `= (30!)/(10! xx 20!)underset(r=0)overset(10)sum(-1)^(r).4^(10-r).(10!)/(r!(10-r)!)` `= .^(30)C_(10)underset(r=0)overset(10)sum(-1)^(r).4^(10-r)..^(10)C_(r)` `= .^(30)C_(10)(4-1)^(10)` `= .^(30)C_(10).3^(10)` |
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