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The value of sum(r=2)^(10) ""^(r)C(2).""...

The value of `sum_(r=2)^(10) ""^(r)C_(2).""^(10)C_(r)` is

A

`10460`

B

`11240`

C

`11520`

D

`12640`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(r=2)overset(10)sum.^(r)C_(2)..^(10)C_(r) = underset(r=2)overset(10)sum(r(r-1))/(2).(10!)/(r!(10-r)!)`
`= 1/2underset(r=2)overset(10)sum(10!)/((r-2)!(10-r)!)`
`= (10 xx9)/(2)underset(r=2)overset(10)sum(8!)/((r-2)!(10-r)!)`
`= 45underset(r=2)overset(10)sum.^(8)C_(r-2)`
`= 45 xx 2^(8)`
`= 11520`
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