Question

Assertion (A): Number of terms in the expansion of $(x+y+z{)}^5$ is 21
Reason (R): The number of terms in the expansion of $(x+y+z{)}^n$ is ${}^{n+2}{C}_2$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true, but R is not the correct explanation of A
• C. A is true, but R is false
• D. A is false, but R is true

Answer 1

Answer: (A)

Both A and R are true and R is the correct explanation of A

We can consider it as a distribution of n things among three in which each can get any number of things including 0 and all.

so it will have a solution as

${}^{n+3-1}{C}_{3-1}$=${}^{n+2}{C}_r$

And for $n=5$

It will be ${}^{5+3-1}{C}_{3-1}$=${}^7{C}_2$ $=21$