#rosen , #counting , #5.1 , 41(a)

Question

in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people , if

a) the bride must next to the groom

my solution is since given that bride and groom must be next to each other then now we have to select 4 person from 8 that is 8c4 now we have to arrange these people since bride and groom next to each other then take BG as one block and rest four __ , __ , __ , __ ,

now arranging BG , __ , __ ,__, __ will take 5! , and arranging BG mutually is 2! ,

so total ways is 8c4*5!*2!

but answer is given 240 (rosen )

Comments

@ papesh

Answer for a and c are correct

Answer for b should be 8C4 * 6! because it is not necessary that bride and groom should be together in the picture. Condition is that bride and groom should be present in the picture.

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47th ans are;  

B:bride   G:groom

a.   

BG -----  BG   -----    BG   -----   BG  -----  BG

we have 5 places where we can arrange BG OR GB 

And remaining 4 can be arranged 4! way.

5C1 * 4! *2! =120 *2 =240

b.

Total ways to arrange 6 peoples - a.  = 6! -240 =480

c.

-----    G(5)  -----  G(4) -----    G (3)  -----   G(2) -----  G (1)

There are 5 places where groom can be placed.

if we place groom at position 1, we have 5 places where the bride can be placed and other 4 can be arranged 4! way.

 5c1 * 4!.

same way if we place groom at position 2, we have 4 places where the bride can be placed and other 4 can be arranged 4! way.

4c1 * 4!.

so the  answer  = 5c1 * 4! + 4c1 * 4! + 3c1 * 4! + 2c1 * 4! + 1c1 * 4!

                       =4!(5+4+3+2+1)

                       =24 * 15 

                       = 360

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@Archies09 thanks..