Answer is 66(when at most 10 roses can be given to a girl)
this is stars and bars question,
if we have 10 roses kept linearly on a table then we will need 2 bars to divide roses in 3 parts.
n (roses) = 10
m(bars) = 2
Use the formula m+nCn hence we get 12C2 = 66
Answer is 36 (when at least 1 rose is distributed among all girls)
Number of ways in which n identical things can be divided into r groups, if blank groups are not 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 1,2 or more items
= (n-1)C(r-1)
Apart from this formula you can think logically that if 1st girl gets only one rose then other two can get a sum of 9 flowers which can be
Girl 1 |
Girl 2 |
Girl 3 |
1 |
1 |
8 |
1 |
2 |
7 |
1 |
3 |
6 |
1 |
4 |
5 |
1 |
5 |
4 |
1 |
6 |
3 |
1 |
7 |
2 |
1 |
8 |
1 |
and if 1st girl gets 2 roses then number of combination decreases by 1
Girl 1 |
Girl 2 |
Girl 3 |
2 |
1 |
7 |
2 |
2 |
6 |
2 |
3 |
5 |
2 |
4 |
4 |
2 |
5 |
3 |
2 |
6 |
2 |
2 |
7 |
1 |
if 1st girl get 3 roses again the combination will go down by one
Girl 1 |
Girl 2 |
Girl 3 |
3 |
1 |
6 |
3 |
2 |
5 |
3 |
3 |
4 |
3 |
4 |
3 |
3 |
5 |
2 |
3 |
6 |
1 |
We can see the combinations are going down as the 1st girl is getting a flower more than the prev one so
total combination with 1st girl having 1 rose = 8
total combination with 1st girl having 2 rose = 7
total combination with 1st girl having 3 rose = 6
total combination with 1st girl having 4 rose = 5
total combination with 1st girl having 5 rose = 4
total combination with 1st girl having 6 rose = 3
total combination with 1st girl having 7 rose = 2
total combination with 1st girl having 8 rose = 1
any girl can have maximum of only 8 roses because other girls must get atleast 1
hence total combinations = 8+7+6+5+4+3+2+1 = 36