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In how many different ways 24 apples can be given to 3 boys and 3 girls if the total number of apples received by boys is a)equal to that received by girls b)double to that received by girls

In how many different ways 24 apples can be given to 3 boys and 3 girls if the total number of apples received by boys is 
a)equal to that received by girls
b)double to that received by girls

Grade:10

1 Answers

Amogh Dasture
48 Points
7 years ago
Case a)
 
It means that 12 apples must be given to boys and 12 to girls
 
Total ways of distributing 12 apples among 3 boys=(n+r-1)C(r-1)= (12+3-1)C(3-1)= 91
Total ways of distributing 12 apples among 3 girls(same as above)=91
 
Hence, total ways = 91x91=8281
 
Case B)
 
Here, 16 apples will be given to boys and 8 to girls
 
No. of ways of distributing 16 apples among 3 boys=153
No. of ways of distributing 8 apples among three girls=45
 
Total no of ways= 153x45=6885
 
Hope it helped

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