**Quote:**

a) 24 ways = First position should be a man so 4 ways second can be 1 way (his wife) so = 4x1x3x1x2x1x1x1 = 24 ways

b) First position can be selected 8 ways and second one only 1 (either man or wife), 3rd can be selected from 6 remaining ways and 4th only 1 way (same logic as above)...etc. So number of ways = 8x1x6x1x4x1x2x1 = 384 ways

c) 1152 ways ===> 2(4x4x3x3x2x2x1x1)

Thoese are all valid

for d, the equation becomes

4! ways of arranging the men

4! ways of arranging the women

2 ways a man and woman can be arranged between themselves

4!*4!*2 = 1152