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InterviewSolution
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Prove that in the expansion of `(1+x)^n(1+y)^n(1+z)^n`, the sum of the coefficients of the terms of degree `ri s^(3n)C_r`.A. `(""^(n)C_(r))^(3)`B. `3 . ""^(n)C_(r)`C. `""^(3n)C_(r)`D. `""^(n)C_(3r)` |
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Answer» Correct Answer - c The given expansion can be written as `ubrace ({( 1+ x) (1 + x) (1 + x)...(1 +x)})_("n - factors") ubrace({( 1 +y)(1 +y) (1 +y)...(1 +y)})_("n - factors")` `ubrace({( 1 +z)(1 +z) (1 +z)...(1 +z)})_("n - factors")` There are 3n factors in this product . To get a term of degree r. we choose r factors out of these 3n factors and then multiply second terms in each factor. there are `""^(3n)C_(r)` such terms each having coefficient 1. Hence, the sum of the coefficients of `""^(3n)C_(r)`. |
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