^404C4-^303C4.^4C1+^202C4.^4C2-^101C4.^4...

`^404C_4-^303C_4.^4C_1+^202C_4.^4C_2-^101C_4.^4C_3=`

`(401)^(4)`

`(101)^(4)`

`0`

`(201)^(4)`

Text Solution

Verified by Experts

The correct Answer is:

The given expression is the coefficient of `x^(4)` in
`.^(4)C_(0)(1+x)^(404)-.^(4)C_(1)(1+x)^(303)+.^(4)C_(2)(1+x)^(202)-.^(4)C_(3)(1+x)^(101)+.^(4)C_(4)`
= Coefficient of`x^(4)` in `[(1+x)^(101)-1]^(4)`
`=` Coefficient of `x^(4)` in `(.^(101)C_(1)x+.^(101)C_(2)x^(2)+".....")^(4)`
`= (101)^(4)`

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