$1.$ A processor has $6$ pipeline stages where the time to complete the operation in each stage is: $1$: $10$ns$,2$: $12$ns$,3$: $15$ns$,4$: $5$ns$,5$: $13$ns$,6$: $8$ns a$.$ How long does one assembly instruction take to run on this processor? b$.$ How long does it take to run a program with $10$ assembly instructions considering single cycle operation $($not pipelined$)?$ c$.$ How long does it take to run the same program with $10$ assembly instructions considering pipelined architecture with no data and control hazards?