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+13 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 (59.4k points)
edited ago by | 2.1k 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

+18 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 Boss (30.6k 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 Loyal (9.2k 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
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