basic doubt

Question

In how many ways can 10 similar roses be distributed among 3 girls?

In how many ways can 10 different roses be distributed among 3 girls?

Answer 1

1) 10 similar roses distributed among 3 girls(girls are different).

     let the 3 girls be x,y,z such that  x+y+z=10 

                                                                = C(n+r-1,r-1)

                                                                =C(12,2) = 66

2)10 different roses distributed to 3 different girls.

     (note : here the funda is to fix the non movable object : fix girls)

1st rose can be given in 3 ways.

2nd rose can be given in 3 ways.

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.

10 roses can be given in 3¹⁰ ways = 59049

 

Comments

here we suppose that let x be a girl and she can get atmost 10 roses , similarly y,z, can also get the same roses.

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and u can do it by combination by making sequeces like {10,0,0} {9,1,0}.........

{8,1,1},{7,2,1}........................................... there will bemore combinations where you can make arrangements and than add all..

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I didn't understand what makes difference in both questions?

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first one says for 10 similar roses..

second one asks for 10 different roses.