four men and four women line up at a checkout counter in a store. In how many different ways can they line up if the first person in line is a man, and the people in line alternate man, woman, man, woman, and so on?

Question

anonymous · Answer

counting principle all the way for these problems

anonymous · Answer

how many choices for the first person in line?

anonymous · Answer

if it is not clear, let me know and we can walk through it slowly (not too slowly)

anonymous · Answer

4

anonymous · Answer

whew ok good
then how many for the second person?

anonymous · Answer

4

anonymous · Answer

right
now we go faster
then 3 then 3, then 2 then 2, then 1 then 1
counting principle says to multiply all this mess together
you can ignore the 1

anonymous · Answer

soooo 576?

anonymous · Answer

final answer is 
$$4\times 4\times 3\times 3\times 2\times 2$$or if you prefer 
$$4!\times 4!$$

anonymous · Answer

okay, thanks

anonymous · Answer

yeah, 576

anonymous · Answer

nice tumblr btw