Question

A child is assembling a model train set. The child has 5 boxcars, 4 flatbed cars, and 3 tank cars. Within type the cars are indistinguishable, i.e., the 5 boxcars are identical in appearance, the 4 flatbed cars are identical in appearance, and the 3 tank cars are identical in appearance. Now suppose the child forms a train by linking these 12 train cars in a line.

a) In how many ways can the train cars be arranged in a line if there is no restriction on the order?

b) In how many ways can the train cars be arranged in a line if the 5 boxcars must be together?

c) In how many ways can the train cars be arranged in a line if the 5 boxcars must be together and the 3 tank cars must be together?

d) In how many ways can the train cars be arranged in a line if each set of train cars of a particular type (box, flatbed, tank) must be together?

Answer 1

a)Number of ways can the train cars be arranged in a line if there is no restriction on the order==27270

b)Number of ways can the train cars be arranged in a line if the 5 boxcars must be together==280

c)Number of ways can the train cars be arranged in a line if the 5 boxcars must be together and the 3 tank cars must be together==30

d)Number of ways can the train cars be arranged in a line if each set of train cars of a particular type (box, flatbed, tank) must be together=3!=6.