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AP EAMCET2005MathematicsBinomial Theorem

The coefficient of x^3 y^4 z^5 in the expansion of (x y+y z+x z)^6 is

Options

  1. A70
  2. B60
  3. C50
  4. DNone of these

Correct answer

B. 60

Step-by-step solution

We have aligned (x y+y z+z x)^6 & = _ r+s+t=6 6 ! r ! s ! t ! (x y)^r(y z)^s(z x)^t & = _ r+s+t=6 6 ! r ! s ! t ! x^ r+t y^ r+s z^ s+t aligned If the general term in the above expansion. contains x^3 y^4 z^5 , then r+t=3, r+s=4 and s+t=5 Also, r+s+t=6 Solving these equations, we get r=1, s=3, t=2 Coefficient of x^3 y^4 z^5= 6 ! 1 ! 3 ! 2 ! = 6 ! 2 ! 3 ! =60

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