In the expansion of $(1 + x)^{n} . (1 + y)^{n} . (1 + z)^{n}$ the sum of the coefficients of the terms of degree $r$ is

(^{n} C_{r})^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^{3 n} C_{r}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 \times n C_{r}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

n C_{3 r}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $^{3 n} C_{r}$
The given expression contains $3 n$ factors
Using combination to choose $r$ brackets out of $3 n$ brackets for a term of degree $r$ , we get
$^{3 n} C_{r}$
Hence, answer is option B

Suggest Corrections

Similar questions

m

{(1 + x)}^{n} {(1 + y)}^{n} {(1 + z)}^{n}

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

T_{r + 1}

{(1 + x)}^{n + 1} =

T_{r}

T_{r + 1}

{(1 + x)}^{n}

^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}

In the expansion of $(1 + x)^{n} (1 + y)^{n} (1 + z)^{n}$ , the sum of the coefficients of the terms of degree r is

Join BYJU'S Learning Program