Question

Find the number of ways $10$ apples,$5$ oranges and $5$ mangoes can be distributed among three persons,each receiving none, one or more.Assume that the fruits of the same species are all alike.

• A. $28000$
• B. $29106$
• C. $16500$
• D. $64200$

Answer 1

Answer: (B)

$29106$

$10$ Apples

$5$ Oranges

$5$ Mangoes

$x+y+z=0$

$x,y,z\ge 0$

Number of ways of distributon

${}^{12}{C}_2{\times }^7{C}_2{\times }^7{C}_2$

$=66\times 21\times 21=1386\times 21=29106$