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Question

The coefficient of x3y4z5 in the expansion of (xy+yz+xz)6 is


A

70

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B

60

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C

50

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D

none of these

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Solution

The correct option is B

60


Explanation for the correct option:

Given the expression (xy+yz+xz)6

when we expand general term we get
(xy+yz+xz)6=.......+6!a!b!c!(xy)a(yz)b(zx)c

(xy+yz+xz)6=.......+6!a!b!c!xa+cya+bzb+c

On comparing the powers x3y4z5 we get,

a+c=3b+c=5a+b=4 On Solving these equations, we get

⇒a=1,b=3,c=2

Hence coefficient of x3y4z5=6!1!3!2!=60

Hence option B is correct answer


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