The number of ways that $8$beads of different colours be string as necklace, is 

Given: $8$beads of different colours string as necklace 

To find: total no. of ways. 

By using formula $n! = 1.2.3........(n-1) . n$

We use permutation for $n$no of beads $-$ No of beads arranged in $\frac{(n-1)!}{2}$ ways. 

Here, $8$different beads can be arranged in circular form in $(8-1)! = 7!$ ways. Since there is no distinction between the clockwise and anti clockwise arrangement. So the required number of arrangements 

$=\frac{7!}{2}= 2520$

Hence option $\left(a\right) 2520$is correct.