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Solution


Q.

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is         [2024]
1 136  
2 406  
3 142  
4 130  

Ans.

(1)

We have, 21 identical apples.

Let x1,x2 and x3 be the number of apples received by the three children.

∴     x1+x2+x3=21

Now, let x1'=x1-2,x2'=x2-2 and x3'=x3-2

∴    x1'+x2'+x3'=21-6=15

∴    Required number of ways =C3-1 15+3-1

                                                       =C217=136