CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Multinomial Expansion

If the number...

Question

If the number of terms in the expansion of $(x + y + z)^{n}$ is $36$ , then the value of $n$ is

Open in App

Solution

Given expansion $(x + y + z)^{n}$

The number of terms is
$^{n + 3 - 1} C_{3 - 1} = 36 \Rightarrow^{n + 2} C_{2} = 36 \Rightarrow \frac{(n + 2) (n + 1)}{2} = 36 \Rightarrow n^{2} + 3 n + 2 = 72 \Rightarrow n^{2} + 3 n - 70 = 0 \Rightarrow (n + 10) (n - 7) = 0 \Rightarrow n = 7 (∵ n \in N)$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the number of terms in the expansion of

(x + y + z)^{n}

36

, then the value of

n

Q. If the number of terms in the expansion of

(x + y + z)^{n}

231

, then the value of

n

Q. The number of terms in the expansion of

(x + y + z)^{n}

Q. 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}

^{n + 2} C_{2}

Q. If the number of terms in the expansion

(2 x + y)^{n} - (2 x - y)^{n}

is 8, then the value of n is ........... (where n is odd ).

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Multinomial Expansion

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon