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In the expansion of `(x+y+z)^(20)`, which of the followign is False?A. Coefficient of `x^(7)y^(8)z^(7)` is zeroB. total number of distinct terms are `231`C. every term of the form`(20!)/((20-r)!(r-k)!k!)` `x^(20)y^(r-k)z^(k) (r,kepsilonW` and `r,kle20)`D. total number of distinct terms are `221` |
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Answer» Correct Answer - D `(x+y+z)^(20)=sum(20!)/(r_(1)!r_(2)!r_(3)!)x^(r_(1))y^(r_(2))z^(r_(3))` where `r_(1)+r_(2)+r_(3)=20` option (1) : `r_(1)+r_(2)+r_(3)=22gt20` `:.` coefficient of `x^(7)y^(5)z^(7)` is zero Option (2): total number of distinct terms `=^(20+3-1)C_(20)` (3) `(20!)/((20-r)!(r-k)!k!)x^(20-)y^(r-k)z^(k)` `r_(1)=20-r_(1)r_(2)r_(2)=k,r_(3)=k` `r_(1)+r_(2)+r_(3)=20` |
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