First let me give you naive solution and then the proper approach or short cut
There are 10 roses,15 sunflowers , 15 daffodils
Roses |
Sunflowers |
Daffodils |
0 – 10
|
15 – 0 |
15 – 0 |
1 – 9 |
14 – 1 |
14 – 1 |
2 – 8 |
13 – 2 |
13 – 2 |
3 – 7 |
12 – 3 |
12 – 3 |
4 – 6 |
11 – 4 |
11 – 4 |
5 – 5 |
10 – 5 |
10 – 5 |
6 – 4 |
9 – 6 |
9 – 6 |
7 – 3 |
8 – 7 |
8 – 7 |
8 – 2 |
7 – 8 |
7 – 8 |
9 – 1 |
6 – 9 |
6 – 9 |
10 -0 |
5 – 10 |
5 – 10 |
|
4 – 11 |
4 – 11 |
|
3 – 12 |
3 – 12 |
|
2 – 13 |
2 – 13 |
|
1 – 14 |
1 – 14 |
|
0 – 15 |
0 – 15 |
Number ways of distributing Roses = 11
Number ways of distributing Sunflower = 16
Number ways of distributing Daffodils = 16
Total number of ways of distributing flowers = 11*16*16 = 2816
n identical objects can be distributed among kk distinct people in =$^{n+k−1}$$C_n$ ways
Here there are 2 girls. So, k=2
1. 10Roses
So n=10 Substitute in the formula, we get,=$^{10+2−1}$$C_{10}$=11
2. 15 Sunflowers
So, n=15. Substitute in the formula, we get, $^{15+2−1}$$C_{15}$=16
3. 15 Daffodils
So, n=15. Substitute in the formula, we get, $^{15+2−1}$$C_{15}$=16
Total ways = 11∗16∗16=2816.