hi,

see if i can sovle the below question like this?

six children will give presentation one after the other, in some order. Ruth's must come after Luke's(not necessarily immediately after Luke's).how many order are possible.?

i tried it like,

Ruth can take 5 position for presentation (except last poisition) = 5P1 = 5

Luke can take 5 position after ruth's presentation(cant take first position) = 5P1 = 5

rest can take remainng 4 position = 4P4= 24

multiplying all three = 5*5*24 = 600

am i right about my approach?

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.

I have already spoken to you about following the posting format. Write all the options in the question

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the question states not necessarily after

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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