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Question

In how many ways can $$12$$ things be divided equally among $$4$$ persons?


Solution

As there are $$12$$ things that needs to be divided amongst $$4$$ people, so each person would get $$3$$ things.
Number of ways of selecting $$3$$ things out of $$12$$ things for $$1^{st}$$ person =$$ { \  }^{ 12 }{ C }_{ 3 }=220 \text { ways.}$$
Number of ways of selecting $$3$$ things out of $$9$$ things for $$2^{nd}$$ person =$$ { \  }^{ 9 }{ C }_{ 3 }=84 \text { ways.}$$
Number of ways of selecting $$3$$ things out of $$6$$ things for $$3^{rd}$$ person =$$ { \  }^{ 6 }{ C }_{ 3 }=20 \text { ways.}$$
Number of ways of selecting $$3$$ things out of $$3$$ things for $$4^{th}$$ person =$$ { \  }^{ 3 }{ C }_{ 3 }=1 \text { way.}$$
Hence, total number of ways $$=220\times84\times20=369600 \text{ ways.}$$

Maths

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