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The value of ((100),(0))((200),(150))+((...

The value of `((100),(0))((200),(150))+((100),(1))((200),(151))+......+((100),(50))((200),(200))` equals (where `((n),(r ))="^(n)C_(r)`)

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The correct Answer is:
6
`:' .^(200)C_(r) = .^(200)C_(200-r)`
`.^(100)C_(0).^(200)C_(50)+ .^(100)C_(1) .^(200)C_(49)+ .^(100)C_(2) .^(200)C_(48)+…….+ .^(100)C_(50) .^(200)C_(0)`
`=` coefficient of `x^(50)` in `(1 + x)"^(100) (x + 1)^(200)`
`= .^(300)C_(50) rArr (n)/(r) = (300)/(50) = 6`
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