Question

There are unlimited number of identical balls of four different colors. How many arrangements of at most $8$ balls in a row can be made by using them?

• A. $21845$
• B. $87380$
• C. $262140$
• D. none of these

Answer 1

The correct option is B $87380$

$4$ diffrent colours

$8$ balls in a row .

$\Rightarrow$ Number of ways

$={\left(4\right)}^8+{\left(4\right)}^7+{\left(4\right)}^6+{\left(4\right)}^5{+\left(4\right)}^4+{\left(4\right)}^3+{\left(4\right)}^2+{\left(4\right)}^1=\frac{{\left(4\right)}^9-4}{4-1}=\frac{262140}{3}=87380$

Therefore number of ways $=87380$