Maths problem

[Puzzler72]

Ten books can be organised on a shelf how many different ways?

[Aquagility]

I've an idea this may be "Factorial 10", ie 10x9x8x7...

Where's crofter?

[kayakamina]

Fibonacci is the maths wizard!

[08012006]

10 factorial = 3,628,800

[gen2]

Yes it is definitely 10 factorial.

There are 10 ways of choosing the 1st book in the row
There are 9 ways of choosing the 2 nd book in the row
There are 8 ways of choosing the 3 rdbook in the row
There are 7 ways of choosing the 4 th book in the row
There are 6 ways of choosing the 5 th book in the row
There are 5 ways of choosing the 6 th book in the row
There are 4 ways of choosing the 7 th book in the row
There are 3 ways of choosing the 8 th book in the row
There are 2 ways of choosing the 9 th book in the row
There is 1 way of choosing the 10 th book in the row

hence 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways to arrange 10 books on a shelf

[Aquagility]

Why, tell me, can I remember that after sixty years, yet I have no idea what I did yesterday? Why?

[johnalex]

Hi folks - Don't forget that Google has an inbuilt calculator in its search field. 'Factorial 10' is just 3 keystrokes: 10! (Answer is displayed in zero seconds.)

Try this for all the combinations of the National Lottery:
Perm any 6 from 49: 49!/6! (just move the decimal point 59 places to the right). More likely to drown in the bath.

Returning to the books problem, according to my son's bedroom there are 4 ways to arrange just 1 book, including back to front and upside down. Let's not go into all the other possibilities, such as flat, on edge, or leaning at an angle. The likelihood of this room ever being tidied is even greater . . . . N! (Factorial Never )

[johnalex]

Re the Lottery calculation above, sorry I omitted 43!
The correct formula is 49!/43!/6! (Answer 13,983,816)

Same as: (49*48*47*46*45*44)/(6*5*4*3*2*1)

Good Luck!