Two men and four women line up at a checkout counter in a store

Question

Two men and four women line up at a checkout counter in a store.

$a)$ In how many ways can they line up?

$b)$ In how many ways can they line up if the first person line is a woman, and then the line changes by gender $(w, m, w, w, m, w)$?

Answer 1

a) it is $6! = 720$ as you mentioned

b) If the order is $(w, m, w, w, m, w)$, you can permute women and men in $4!$ and $2!$ ways so number of arrangements $= 4! \times 2! = 48$