Sixteen men compete with one another in running, swimming and riding. How many prize lists could be made, if there were altogether $$6$$ prizes of different values, one for running, $$2$$ for swimming and $$3$$ for riding?

Question

Infinity Learn · Accepted Answer

Number of ways of giving one prize for running $$=$$ $$16Number$$ of ways of giving two prizes for swimming $$=16x15Number$$ of ways of giving three prizes for riding $$=16x15x14Required$$ ways of giving prizes $$=16$$×$$16$$×$$15$$×$$16$$×$$15$$×$$14=163$$×$$152$$×$$14$$

Sixteen men compete with one another in running, swimming and riding. How many prize lists could be made, if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?

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