[tex] \large \bold{COMBINATION:}[/tex]
[tex]\large \begin{aligned} \bold{C_k(n) \bigg(\frac {n}{k} \bigg) = \frac{n!}{k!(n-k)!} } \end{aligned} \\ \\ \large\begin{aligned}\bold{n = 7} \\ \bold{k = 8} \end{aligned} \\ \\ \large\begin{aligned} \bold{C_7(8) = \ \bigg(\frac{8}{7} \bigg) = \frac{8!}{7!{(8-7)!} }} \end{aligned} \\ \dashrightarrow{ \boxed{\bold{number \: of \: combination : 8}}}[/tex]
[tex] \bold{Combination\:With\: Repitition :}[/tex]
[tex]\large\begin{aligned}{\bold{C_k^{′}(n) = \bigg( \frac{n + k - 1}{k} \bigg)}}\end{aligned} \\ \\ \large \begin{aligned}{ \bold{n = 7} }\\ \large \bold{k = 8} \end{aligned} \\ \\ \large \begin{aligned}{ \bold{C_8^{′}(7) =C_8(7 + 8 - 1) = C_8(14) = \bigg( \frac{14}{8} \bigg )}} \\ = \large \bold{\frac{14!}{8!(14 - 8)!}} = \large \bold{ \frac{14•13•12•11•10•9}{6•5•4•3•2•1}} \large \bold{= 3003} \\ \bold{\ number \: of \: combination \: with \: repitition : } \underline\bold{3003}\end{aligned} [/tex]
