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+12 votes

Two girls have picked 10 roses, 15 sunflowers and 15 daffodils. What is the number of ways they can divide the flowers among themselves?

  1. 1638
  2. 2100
  3. 2640
  4. None of the above


asked in Combinatory by Veteran (69k points)
retagged by | 1.9k views
In Gate question it's 14 daffodils not 15. After taking 14 daffodils answer is coming (C).
Division and Distribution of Identical Objects
Case 1

Number of ways in which n identical things can be divided into r groups, if blank groups are allowed (here groups are numbered, i.e., distinct)

= Number of ways in which n identical things can be distributed among r persons, each one of them can receive 0,1,2 or more items

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

can we do like this here girls =2  lets  these two girls are two groups   ,  10 roses ,
so   (10 + 2 -1) C(2-1)  =  11   
and so on
There is no clarity in the question, I guess.
why are you considering flowers as identical objects??

3 Answers

+17 votes
Best answer
for each flower, say there are $n$ number of flowers, we apply star and bars method for each flower. $n$ flowers of a type will generate $(n+1)$ spaces we just need to place one bar. to do that we need to select a position.

so, for roses : $\binom{10+1}{1}$
for sunflowers : $\binom{15+1}{1}$
for daffodils : $\binom{15+1}{1}$

total number of ways distribution can take place = $11 \times 16 \times 16 = 2816$
answered by Veteran (31k points)
selected by
+22 votes
answer - D

number of ways roses can be distributed - { (0, 10), (1, 9), (2, 8).....(10, 0) } - 11 ways

similarly sunflowers and daffodils can be distributed in 16 ways each

total number of ways 11 x 16 x 16 = 2816
answered by Boss (9.3k points)
0 votes
For 10 roses no.of ways=n+1= 11 ways

Similarly for 15 sunflowers=  16 ways

And for daffodils no. Of ways= 15 ways

So, total number of ways= 11*16*15=2640 ways

So answer is C
answered by anonymous

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