Find the number of ways 10 apples, 5 oranges & 5 mangoes can be distributed among 3 persons, each receiving zero or more. Assume that the fruits of the same species are alike.

for a particular arrangement of all fruits, no of ways of distributing them is ^n+r-1C_r-1 (blank groups allowed)

= ²²C₂

since all fruits are not alike they can be arranged in a no if ways : 20!/5!5!10!

Total no of ways : ²²C₂ X 20!/5!5!10! = 22!/2!5!5!10!

NUMBER OF WAYS OF DIVIDING 10 APPLES AMONG 3 PEOPLE= NO OF SOLUTIONS OF THE EQUATION x+y+z=10 where x,y,z greater than or equals to 0 which is equals to  ¹²C_2.  similiarily no of ways of distributing 5 oranges= ⁷c₂ mangoes =  ⁷C₂

total ways = ¹²C₂ * 7c2 *7c2