GATE | GATE CS 1999 | Question 27

Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers amongst  themselves?
(A) 1638
(B) 2100
(C) 2640
(D) None of the above


Answer: (C)

Explanation: Assume the two girls only have 10 roses. They can share these in (11 choose 1) = ¹¹C₁ = 11 ways.
Similarly, they can share 15 sunflowers and 14 daffodils in
(15 choose 1) = ¹⁵C₁ = 16 ways
(14 choose 1) = ¹⁴C₁ = 15 ways
So, they can share all the flowers in 11 * 16 * 15 = 2640 ways
So, option (C) is correct.

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