Question

Evaluate the following expression Express your answer as a fraction or a decimal number rounded to four decimal places13P8 ÷ 13C7

Answer 1

30,240

Step-by-step explanation:

We were given the expression:

`(13P_8)/(13C_7)`

We will simplify the expression as shown below:

`\begin{gathered} (13P_(8))/(13C_(7)) \\ \text{For Permutation, we have:} \\ nP_r=\frac{n!{}}{(n-r)!} \\ 13P_8=\frac{{13!}}{(13-8)!}=(13!)/(5!) \\ 13P_8=(13*12*11*10*9*8*7*6*5!)/(5!) \\ 13P_8=13*12*11*10*9*8*7*6 \\ 13P_8=51,891,840 \\ \\ \begin{equation*} 13C_7 \end{equation*} \\ \text{For Combination, we have:} \\ nC_r=(n!)/(r!(n-r)!) \\ 13C_7=(13!)/(7!(13-7)!)=(13!)/(7!6!) \\ 13C_7=(13*12*11*10*9*8*7!)/(7!*6*5*4*3*2*1) \\ 13C_7=(13*12*11*10*9*8)/(6*5*4*3*2*1) \\ 13C_7=(1,235,520)/(720) \\ 13C_7=1,716 \\ \\ \Rightarrow(13P_(8))/(13C_(7))=(51,891,840)/(1,716)=30,240 \\ (13P_8)/(13C_7)=30,240 \\ \\ \therefore(13P_(8))/(13C_(7))=30,240 \end{gathered}`