Question

There are unlimited number of identical balls of three different colours. How many arrangements of almost 7 ball in a row can be made by using them?

• A. 2187
• B. 343
• C. 399
• D. 3279

Answer 1

The correct option is D 3279

There is an unlimited number of identical of three rows.

Number of arrangement of 7 balls in a row $=3^7$

Number of arrangement of 6 balls in a row $=3^6$

Number of arrangement of 5 balls in a row $=3^5$

Number of arrangement of 4 balls in a row $=3^4$

Number of arrangement of 3 balls in a row $=3^3$

Number of arrangement of 2 balls in a row $=3^2$

Number of arrangement of 1 balls in a row $=3$

$\therefore$ Number of arrangement of almost 7 balls in row that can be made $\left(n\right)=3+3^2+3^3+3^4+3^5+3^6+3^7$

As it is in GP

$n=\frac{3(3^7-1)}{3-1}$

$=\frac{3}{2}(2187-1)$

$=\frac{3}{2}\times 2186$

$=3\times 1093$

$n=3279$