Question

Introduction to permutations and combinationsSuppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.(a)How many ways can this be done, if the order of the choices is taken intoconsideration?0How many ways can this be done, if the order of the choices is not taken into(b) consideration?I need help with this math problem

Answer 1

Part a. If the order is taken into consideration, we use Permutation of 2 letters from a set of 4 letters. So, we have

`_4P_2=(4!)/((4-2)!)=12`

Part b. If the order doesnt matter, we use Combinations of 2 letters from a set of 4 letters, that is,

`4C_2=(4!)/(2!(4-2)!)=6`

Therefore, the answers are:

`\begin{gathered} a)\text{ 12} \\ b)\text{ 6} \end{gathered}`