Sheldon Ross Chapter 1 Example 3c

Question

Ms. Jones has 10 books that she is going to put on her bookshelf. Of these, 4 are mathematics books, 3 are chemistry books, 2 are history books, and 1 is a language book. Ms. Jones wants to arrange her books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible?

Please provide a different explanation rather than the textbook one.

Answer 1

Assume books are M1,M2,M3,M3,C1,C2,C3,H1.H2,H3,L1

Now assume that i need a permutations of above word where I want all M prefixes alphabet together ,All C prefixes alphabet together ,All H prefixes alphabet together,All L prefixes words together.

So if something is together consider it as a word.So i can say I need a permutation of a word MCHL,M means all M1,M2,M3,M4.Same for others.

So i can have 4! permutations of MCHL . Now the M itself has 4 objects M1,M2,M3,M4 which can permute in 4! ways,Similarly C,H,L can permute among themselves.

So toal answer will be 4!*(4!*3!*2!*1!) = 6912 should be the correct answer

Comments

but if those 4 mathematics book and  same for remaining others are same then answer will be only 4 ! na correct if i am wrong

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Yes.Then permutation will become combination