Two girls have picked 10 roses, 15 sunflowers, and 14 daffodils. Assuming…
1999
Two girls have picked 10 roses, 15 sunflowers, and 14 daffodils. Assuming flowers of the same type are identical and a girl may receive zero flowers of a particular type, in how many ways can they divide all the flowers among themselves?
- A.
1638
- B.
2100
- C.
2640
- D.
None of the above
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Key idea: choose how many flowers of each type one girl receives. The other girl then automatically receives the remaining flowers.
Roses: 0, 1, 2, ..., 10 gives
11choices.Sunflowers: 0, 1, 2, ..., 15 gives
16choices.Daffodils: 0, 1, 2, ..., 14 gives
15choices.
Zero is included because the question does not require each girl to receive at least one flower of every type; one girl may receive all flowers of a type and the other may receive none of that type.
Total ways: 11 x 16 x 15 = 2640.