Question

${\sum }_{i=0}^n{\sum }_{j=0}^n{\sum }_{k=0}^n{(}^n{C}_i\left){(}^n{C}_j\right){(}^n{C}_k)$ The value of the expression

• A. is less than 500, if n = 3
• B. is greater than 600, if n = 3
• C. is less than 5000, if n = 4
• D. is greater than 4000, if n = 4

Answer 1

Answer: (C), (D)

The correct options are
C is less than 5000, if n = 4
D is greater than 4000, if n = 4

${\sum }_{i=0}^n{\sum }_{j=0}^n{\sum }_{k=0}^n{(}^n{C}_i\left){(}^n{C}_j\right){(}^n{C}_k)$

$\Rightarrow \left[{\sum }_{i=0}^n{(}^n{C}_i\right)]\left[{\sum }_{j=0}^n{(}^n{C}_j\right)]\left[{\sum }_{k=0}^n{(}^n{C}_k\right)]=2^{3n}$