Question

Prob 4.b. (5 pt) An annual family picture following Thanksgiving dinner is arranged with all 8 family members in a row in front of a fireplace.
a)How many different arrangements of family members are possible?

b) Suppose the family includes four males and four females. What is the probability that the radom arrangement will alternate male, female, male, female, etc? (Note the arrangement starts with male.)

Answer 1

Here we have

8 family members in a row in front of a fireplace.

(a)There are n! ways to arrange n people in a row.

So the required number of ways=8!=8x7x6x5x4x3x2x1=40320

(b)4 Male and 4 female can be seated alternately in 4!*4!ways
BGBGBGBG - 4!*4! (4 Male can be arranged in their slots in 4! ways and similarly 4 women can be arranged in their slots in 4! ways)=(4x3x2x1)*(4x3x2x1)=576