Given:
The expression is given as,
[tex]\frac{^8C_3}{^8P_3}\text{ . . . . .. (1)}[/tex]
The objective is to evaluate the expression.
Explanation:
The general formula of permutation and combination are,
[tex]\begin{gathered} ^nC_r=\frac{n!}{(n-r)!r!}\ldots\text{.}\mathrm{}(2)_{} \\ ^nP_r=\frac{n!}{(n-P)!}\ldots..(3) \end{gathered}[/tex]
Using equations (2) and (3) in equation (1),
[tex]\frac{^8C_3}{^8P_3}=\frac{\frac{8!}{(8-3)!3!}}{\frac{8!}{(8-3)!}}[/tex]
On further solving the above equation,
[tex]\begin{gathered} =\frac{\frac{8!}{3!}}{8!} \\ =\frac{1}{3!} \\ =\frac{1}{3\times2\times1} \\ =\frac{1}{6} \end{gathered}[/tex]
Hence, the value of the expression is 1/6.
