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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.

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.

Grade:10

2 Answers

nikhil arora
54 Points
10 years ago

for a particular arrangement of all fruits, no of ways of distributing them is n+r-1Cr-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!

kushal satya
37 Points
10 years ago

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  12C2.  similiarily no of ways of distributing 5 oranges= 7c2 mangoes =  7C2

total ways = 12C2 * 7c2 *7c2  

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