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  • Find the total number of terms in the expansion of <img alt="\mathrm{\left (x_1+x_2+x_3+x_4+x_5 \right )}^8" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft%20%28x_1&am

Find the total number of terms in the expansion of \mathrm{\left (x_1+x_2+x_3+x_4+x_5 \right )}^8

Option: 1

495


Option: 2

792


Option: 3

330


Option: 4

715


Answers (1)

best_answer

Multinomial Theorem

The number of distinct terms in the multinomial expansion \mathrm{\left (x_1+x_2+x_3+........+x_k \right )}^n is  n + k - 1Ck - 1. 

 

Now,

Total number of terms is 

^{n + k - 1}C_{k - 1}=\;^{8 + 5 - 1}C_{5 - 1}\\\\\;^{12}C_{4}=\frac{12!}{4!8!}=\frac{12\times11\times10\times9}{4\times3\times2\times1}=495

 

hence option A is correct

Posted by

Gautam harsolia

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