Question

In a lucky draw, ten names are out in a box out of which three are to be taken out. Find the number of total ways in which we can take four names out.

Answer 1

Step 1

Given;

Required; To find the number of ways in which we can take out four names

Step 2

Find the number of total ways in which we can take four names out.​

Here, we will take out three names. Thus selection is four without having botheration about ordering the selection.

Thus, the possible number of ways for finding three names out of ten from the box will be :

`nC_r=(n!)/(r!(n-r)!)`

where;

`\begin{gathered} n=10 \\ r=4 \end{gathered}`
`nCr=(10!)/(4!(10-4)!)`
`nCr=(3628800)/(24(720))=210\text{ ways}`

Answer;

`210\text{ ways}`