2 A kid is playing with his 12 stuffed animals a If he wants

(2) A kid is playing with his 12 stuffed animals.

a. If he wants to line them up, how many different lines can he form.

b. Suppose the 12 animals consist of 5 bears 7 alligators, and he wants to put the same species together, how many lines can he form with the 12.

c. ore condition in part b. Suppose the bears are identical and the alligators are identical, how many distinguishable lines can he form.

Solution

a) Assuming all the animals are different;

he can form 12P12 = 12! different lines;

b) suppose; 5 bear and 7 alligators;

take 5 bears together and 7 alligators;

(5! * 7! ) 2!;

c)

if bears and alligators are identical;5C5 * 7C7 * 2! = 2; distinct lines can be formed;