Question

find both the number of combinations and the number of permutations for five objects Taken 2 at a time

Answer 1

Given: 5 objects taken 2 at a time

`\begin{gathered} \text{Permutation} \\ _5P_2=(n!)/((n-r)!)=(5!)/((5-2)!)=(5\cdot4\cdot3\cdot2\cdot1)/(3!)=(120)/(3\cdot2\cdot1)=(120)/(6)=20 \\ \\ \\ \text{Combination} \\ _5C_2=(n!)/(r!(n-r)!)=(5!)/(2!(5-2)!)=(5\cdot4\cdot3\cdot2\cdot1)/(2!\cdot3!)=(120)/((2\cdot1)(3\cdot2\cdot1))=(120)/(12)=10 \end{gathered}`