wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The coefficient of xnyn in the expansion of {(1+x)(1+y)(x+y)}n is

A
nr=0Cr2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
nr=0Cr3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
nr+s=0nCrnCs2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B nr=0Cr3
We have,
{(1+x)(1+y)(x+y)}n
=(C0+C1x+C2x2++Cnxn)× (C0yn+C1yn1+C2yn2++Cn1y+Cn)× (C0xn+C1xn1y++Cn1xyn1+Cnyn)

If we multiply them , each vertical column will be the term of xnyn
Coefficient of xnyn on R.H.S
=C03+C13+C23++Cn3
=nr=0Cr3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon