You can use Binomial Theorem to solve this:
P(each user being active) = $\frac{1}{10}$
P(each user not being active) = $\frac{9}{10}$
P(exactly $8$ users are active/ are transmitting at the same time):
- Out of $10$ users we can select any $8$ users = $_{}^{10}\textrm{}C_{8}$
- $8$ users transmitting successfully/ are active = $(\frac{1}{10})^8$
- $2$ users not being active/ not transmitting = $(\frac{9}{10})^2$
P = $_{}^{10}\textrm{}C_{8}$ x $(\frac{1}{10})^8$ x $(\frac{9}{10})^2$
= $45$ x $10^{-10}$ x 81
= $3645$ x $10^{-10}$
So we need to find out $10^{10}$ x P = $3645$.
Both Packet and Circuit Switching will give the same answer.