Question

Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers among themselves?

• A. 1638
• B. 2100
• C. 2640
• D. None of these

Answer 1

The correct option is C 2640

Number of ways for distributing r similar things among n diffrent things = ${}^{(n-1+r)}{C}_r$
The number of ways for distributing 10 roses among the two girls = ${}^{(2-1+10)}{C}_{10}=11$
Similarly number of ways for distributing 15 sunflowers among two girls = ${}^{(2-1+15)}{C}_{15}$
${=}^{16}{C}_{15}{=}^{16}{C}_1=16$
Number of ways for distributing 14 daffodils among the two girls
${=}^{(2-1+14)}{C}_{14}{=}^{15}{C}_{14}{=}^{15}{C}_1=15$
therefore Total number of ways = $11\times 16\times 15=2640$