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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?
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+1 vote

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

by Boss (12.2k points)
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hey 10^3 would not be in 2nd case because it dependent???
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yes fix the non movable objects or you can say fix the more important thing(in laymans language).

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and if u break 10^3 it means 1st girl given to 10 rose.......... how is this possible.
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movable means?? will you please explain
+1
Its just a layman concept : see a rose can be moved easily... But not a girl.

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Similarly in case of ring and finger.

Ring can be moved easily in fingers.
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"let the 3 girls be x,y,z such that  x+y+z=10"

I didn't understand this. Can you please do 1st part without using formula. Please
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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.