Question

Im having trouble solving these type of problems i dont know how to plus in the numbers

Answer 1

Given:

The expression is given as,

`(^8C_3)/(^8P_3)\text{ . . . . .. (1)}`

The objective is to evaluate the expression.

Step-by-step explanation:

The general formula of permutation and combination are,

`\begin{gathered} ^nC_r=(n!)/((n-r)!r!)\ldots\text{.}\mathrm{}(2)_{} \\ ^nP_r=(n!)/((n-P)!)\ldots..(3) \end{gathered}`

Using equations (2) and (3) in equation (1),

`(^8C_3)/(^8P_3)=((8!)/((8-3)!3!))/((8!)/((8-3)!))`

On further solving the above equation,

`\begin{gathered} =((8!)/(3!))/(8!) \\ =(1)/(3!) \\ =(1)/(3*2*1) \\ =(1)/(6) \end{gathered}`

Hence, the value of the expression is 1/6.