Question

In how many ways 2 balls can be chosen from 5 balls from an urn?A.2 waysB.20 waysC.5 waysD.10 ways

Answer 1

We have 5 balls, lets name each one:

`\text{Balls}=\mleft\lbrace A,B,C,D,E\mright\rbrace`

Now, we want to take 2 balls at a time, wich means the the order that i take the ball doesnt matter, so lets see the possibilities:

`\mleft\lbrace A,B\mright\rbrace,\mleft\lbrace A,C\mright\rbrace,\mleft\lbrace A,D\mright\rbrace,\mleft\lbrace A,E\mright\rbrace,\mleft\lbrace B,C\mright\rbrace,\mleft\lbrace B,D\mright\rbrace,\mleft\lbrace B,E\mright\rbrace,\mleft\lbrace C,D\mright\rbrace,\mleft\lbrace C,E\mright\rbrace\text{ or }\lbrace D,E\rbrace\text{ }`

So, we have 10 ways to take 2 balls from 5 balls.

If want to solve the formula, we just need to remember the formula for the combinations of 5 elements taking 2:

`\text{Combinatories n taking k }=(n!)/(k!(n-k)!)\rightarrow\text{Combinatories 5 taking 2 }=(5!)/(2!(3)!)=(20)/(2)=10`