Question

Which is greater 4 P 3 or 4 C 3?

Answer 1

`nPr = (n!)/((n-r)!) \\ \\ nCr = (n!)/(r!(n-r)!)\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}`

Answer 2

`\large\boxed{_4P_3>_4C_3}`

Explanation:

`\left\begin{array}{ccc}_nP_r=(n!)/((n-r)!)\\\\_nC_r=(n!)/(r!(n-r)!)\end{array}\right\}\Rightarrow(n!)/((n-r)!)>(n^!)/(r!(n-r)!)\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)!`

`\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=(4!)/((4-3)!)=(1\cdot2\cdot3\cdot4)/(1!)=(24)/(1)=24\\\\_4C_3=(4!)/(3!(4-3)!)=(1\cdot2\cdot3\cdot4)/(1\cdot2\cdot3\cdot1!)=(24)/(6)=4\\\\24>4\Rightarrow_4P_3>_4C_3`