# MATES

In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?

Correct result:

n =  324632

#### Solution:

$n={C}_{5}\left(35\right)=\left(\genfrac{}{}{0px}{}{35}{5}\right)=\frac{35!}{5!\left(35-5\right)!}=\frac{35\cdot 34\cdot 33\cdot 32\cdot 31}{5\cdot 4\cdot 3\cdot 2\cdot 1}=324632$

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