Question

The coefficient of a^7b^c^3in the expansion of (2ab+bc-ca)^7 is:

(A)-560

(C)-280

(B) 560

(D) 280​

Answer 1

Correct option is

C

120

The general term in the expansion of (bc+ca+ab)

10

is

r!s!t!

10!

(bc)

r

(ca)

s

(ab)

t

=

r!s!t!

10!

a

s+t

b

r+t

c

r+s

where r+s+t=10

For the coefficient of a

10

b

7

c

3

we take s+t=10,r+t=7,r+s=3

Since r+s+t=10 we get r=0,s=3,t=7

Thus, the coefficient of a

10

b

7

c

3

in the expansion of (bc+ca+ab)

10

is

=

0!3!7!

10!

=

1×3×2

10×9×8

=120