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The value of sum(r=0)^(10)r""^(10)C(r)3^...

The value of `sum_(r=0)^(10)r""^(10)C_(r)3^(r)(-2)^(10-r)` is

A

20

B

10

C

300

D

30

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(r=0)overset(10)sumr^(10)C_(r)3^(r)(-2)^(10-r)= 10 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r)(-2)^(10-r)`
`= 10 xx 3 underset(r=0)overset(10)sum.^(9)C_(r-1)3^(r-1)(-2)^(10-r)`
`= 30(3-2)^(9) = 30`
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