[Math] A boat is to be manned by 8 men,of whom 2 can only row on bow side & 1 can only row on stroke side;in how many ways can the crew be arranged

Question

I tried it by selecting 2 men out of 8 for bow side,and then arrange them in 2! ways.This can be done in$ \binom{8}{2}$*2! ways,and the stroke side can be crewed in 6 ways.So the required no. of ways are $\binom{8}{2}$*2!*6=336.
But,my answer is not matching.It's correct answer is 5760.

Please help me in pointing out my mistake.

Answer 1

See we don't want to select people we want to arrange people. Hence total ways are $^4P_2\times$$^4P_1\times$$^5P_5=5760$ assuming boat has 4 rowing on each side.