Question

There are unlimited number of identical balls of four different colours. The number of arrangements of at most 8 balls in a row that can be made by using them is:

• A. 83780
• B. 87830
• C. 87380
• D. 87308

Answer 1

The correct option is C 87380

At most - $8$ balls

$8,7,6,5,4,3,2,1$

Let Colours $B,4$ Black, Red

$(4^8+4^7{4}^6+4^5=4^3+4^2=4^1)$

$=Sn={}^a\frac{\left(r^n-1\right)}{\left(r-1\right)}$

$=\frac{4(4^8-1}{4-1}=\frac{4}{3}(65536-1)$

$\frac{4\left(65535\right)}{3}$

$=87380$

Hence, this is the answer.