Wrong explanation scroll down

There are 6 children say Eddy, Freddy, Teddy, Kiddie, Luke and Ruth.

Now Ruth must come after luke so we can combine them into one unit (Luke+Ruth). Now the problem becomes arranging Eddy, Freddy, Teddy, Kiddie , Luke+Ruth (5 objects).

You can arrange 5 objects in 5! ways or 120.

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Sandy
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Hey you are right. The new explanation.

Let us investigate Luke at different positions.

For example:
Luke at Position 1: Ruth can be at 5 different positions and other 4 can be at any position that available after Ruth.

Lukes Position	Number of options for Ruths Position	Number of ways to arrange the Remaining 4
Position 1	5	4!
Position 2	4	4!
Position 3	3	4!
Position 4	2	4!
Position 5	1	4!
Position 6	0	4!

Thus total number of ways of arrangement = \((5+4+3+2+1+0)*4!=360\).

Thanks for the correction.
Regards
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Sandy
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