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  4. The number of ways in which 18 identical coins can be distributed among five children A, B, C, D and E so that everyone gets atleast one coin but not more than 8 coins, is

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Q. The number of ways in which 18 identical coins can be distributed among five children A, B, C, D and E so that everyone gets atleast one coin but not more than 8 coins, is

Permutations and Combinations

Solution:

Giving one to each we have 13 coins to be distributed in 5 children.
OOOOOOOOOOOOOOØØØØ
using beggar ${ }^{17} C _4$ ways
Now, give 8 more to $A$ or $B$ or $C$ or $D$ or $E$ we have number of ways to be rejected
$\text { ОООООØØØ Ø=5. }{ }^9 C _4$
Required ways $={ }^{17} C _4-5 \cdot{ }^9 C _4=2380-630=1750$ ways