Question

3. C(8, r) = 28; r =​

Answer 1

Given:

`C(8,r)=28`

To find:

The value of r.

Solution:

Combination formula:

`C(n,r)=(n!)/(r!(n-r)!)`

We have,

`C(8,r)=28`

Using the combination formula, we get

`(8!)/(r!(8-r)!)=28`

`(8!)/(28)=r!(8-r)!`

`(8* 7* 6!)/(28)=r!(8-r)!`

`2* 6!=r!(8-r)!`

It can be written as:

`2!6!=r!(8-r)!`
`[\because 2!=2* 1=2]`

Case 1:

`2!=r!`

`r=2`

And,

`6!=(8-r)!`

`6=8-r`

`r=8-6`

`r=2`

Case 2:

`6!=r!`

`r=6`

And,

`2!=(8-r)!`

`2=8-r`

`r=8-2`

`r=6`

Therefore, the value of r is either 2 or 6.