$[6]$ We have two binary symmetric channels $1$ & $2.$

Channel $1$ has an error probability of $0\mathrm{.}12$ and channel $2$ has an error probability of $0\mathrm{.}23.$

a$)[4]$ If we want to transmit a bit sequence of ten bits, for each channel $($channel $1$ and channel $2),$ what is the probability $($with four decimal places$)$ that:

A two$-$bit error occurs?

A three$-$bit error occurs?

b$)[2]$ If the source can transmit at $120$ kbit per second for each channel $($channel $1$ and channel $2),$ what is the maximum number of information bits per second that we can transmit through each channel $($channel $1$ and channel $2)$ if we want to be able to transmit the information bits reliably? Please give your answer with the unit in kbit per second $($with four decimal places$).($k $=10)$