CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

In the expansion of (1+x)n(1+y)n(1+z)n, the sum of coefficients of the terms of degree ‘r’ is


  1. 3nCr

  2. 3.nCr

  3. 3nC3r

  4. 3nC3nr


Solution

The correct options are
A

3nCr


D

3nC3nr


(1+x)n(1+y)n(1+z)n(nm=0 nCmxm)(ns=0 nCsys)(nt=0 nCtzt)=0r, s, tn nCm nCs nCt XmYsZt

 For sum of the coefficients of degree ‘r’, we have m + s + t = r; where, m, s, t are integers greater than or equal to zero. Sum of such coefficients

=m,s,t0m+s+t=rnCm n Cs nCt (this is similar to the number of ways of choosing a total of r balls out of n black, n white, n green balls.) =3nCr  

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
QuestionImage
QuestionImage
View More...


People also searched for
QuestionImage
QuestionImage
View More...



footer-image