Answer : (a) 5040 b) 720 c) 288
Step-to step explanation:-
Given : There are 3 Computer Science, 2 Mathematics, and 2 Sociology textbooks.
Total books = 7
a) The number of ways the books can be arranged in any order is given by :-
[tex]7!=7\times6\times5\times4\times3\times2=5040[/tex]
b) We consider all computer books as one thing, then, the total number of things to arrange = 1+2+2=5
Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-
[tex]3!\times5!\\\\=6\times120=720[/tex]
c) We consider all computer books as one thing and math book as one thing, then, the total number of things to arrange = 1+1+2=4
Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-
[tex]4!\times 3!\times2!=24\times6\times2=288[/tex]
