Question

There are four different math books, six statistics and two physics books which should be accommodated in a bookstore. In how many ways can you order if:
a) There is no restriction
b) The books of each topic must be together
c) Only math books should be together

Answer 1

a) number of ways to arrange 12 books in order =12! =479001600

b) number of ways =N(arrange 4 math book in order, 6 stat book in order and two physics book in order and arrange 3 subject in order) =4!*6!*2!*3!=24*720*2*6 =207360

c)

number of ways =N(math book in order)-N(math and stat book in order)-N(Math and physics book in order)+P(all three subject books are in order)

=9!*4!-4!*4!*6!-8!*4!*2!+207360

=8709120-414720-1935360+207360

=6566400