Question

There are 10 books on C Programing, 9 books on Python Programing and 8 books on Fortran Programing. In how many ways can these books be arranged on a shelf if

(a) the books can be arranged in any order?

(b) the Python books must be together and the C books must be together?

(c) The C books must be together but the Python and Fortran books can be arranged in any order?

Answer 1

a) In all we have 10 + 9 + 8 = 27 books.

These can be arranged in any order.

Therefore, for the first book we have 27 choices, for the second book we are left with 26 choices, for the third we have 25 choices remaining and so on.

Therefore, total number of ways = 27 × 26 × 25 × ... × 1 = 27!

b) Now, python and C books must be together. Considering them as 1 unit each. Total number of books = 1 + 1 + 8 = 10.

Therefore, number of ways of arranging these 10 books = 10! (From part a).

Now, the 10 books on C can be arranged withing itself in 10! ways, whereas, python books can be arranged within itself in 9! ways.

Therefore, total number of ways = 10! × 10! × 9!

c) Considering C books as one unit and using the similar approach as part b, Total number of ways = 18! × 10!