Question

John draws a regular five pointed star in the sand, and at each of the 5 outward-pointing points and 5 inward-pointing points he places one of ten different sea shells. How many ways can he place the shells, if reflections and rotations of an arrangement are considered equivalent?

Answer 1

Answer is 362880

Explanation:

10!/10 = 362880!

Answer 2

Solution : Given points to be fill are : 5 external points + 5 internal points

Total positions to be fill are 5+5 = 10

given number of sea shell to be placed are = 10

Here all sea shell are different so each sea shell is different from any other sea shell

if we interchange the position of any two sea shell we would be getting totally different

arrangement .

We can think this problem like 10 sea shell are to be placed at 10 different places

We start with placing first sea shell .

In the beginning we have 10 positions

once it is placed we pick second sea shell and now we have only 9 vacant places

once it is placed we pick next ses shell and we have 8 vacant places for it

we continue with it till we place the last sea shell for which we would be having

only 1 vacant place.

This way the total number of arrangements we get : 10x9x8x7x6x5x4x3x2x1 = 3628800

ANSWER = 3628800