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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