library shelf question?

Question

a library shelf contains 7 different books. In how many ways can they be arranged if
a) no restrictions
b) the mathematics of data management textbook must be first
c) the three mathematics texts must be together

Answer 1

a) 7! = 5040 { This assumes all books are unique }

b) 6! = 720 { First book is placed, and then the other six in any order }

c) 5! * 3! = 720 { The three mathematics books are considered to be one item, but they can be ordered within themselves }

Answer 2

The way to figure this is to look at it mathematically.

There are 7 possiblities for the first book, 6 for the next and 5 for the next etc. So your math looks like this


7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

Now, if you take away the first choice, then it leaves only 6 books left for the rest so your math would be

1 * 6 * 5 * 4 * 3 * 2 * 1 = 720

If the three of the books must be together, AND you want the most options, putting them at the end garners this
4 * 3 * 2 * 1 * (3 * 2 * 1)= 144
(Note that the three books only need be put together, yet they can offer up 6 variations of placement.

Answer 3

a. 7!
b. 6!
c. The 3 math texts can be arranged in 3! ways. They may start at any of five positions (1, 2, 3, 4, or 5; but not 6 or 7).
The remaining 4 books can be arranged in 4! ways. Answer: (3!)(5)(4!)

Answer 4

a) 7!
b) 6!
c) (123)(234)(345)(456)(567)..........
5 diff ways