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Question

The coefficient ofa3b4c5 in (bc+ca+ab)6 is


A

60

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B

50

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C

40

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D

120

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Solution

The correct option is A

60


[If n is a positive integer and a1a2a3........am C then
(a1+a2+a3+.....am)n=n!n1!n2!.......nm!a1n1a2n2a3n3.....amnm where n1n2n3....nm are all non-negative integers subject to the condition n1+n2+n3+.....+nm=n]
a3b4c5=(ab)x(bc)y(ca)z
=az+xbx+ycy+z
z+x=3, x+y=4, y+z=5 x+y+z=6
then x=1, y=3, z=2
The co-efficient of a3b4c5=6!1!2!3!=60


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