Multiplication Rule application condition As we know that multiplication rule states that number of  tasks can be done in $a_{1}*a_{2}..*a_{z}$ ways where one task is done is $a_{1}$ ways , another task in $a_{2}$ ways... , where $z$ represents how many task being performed . I would like to know if the tasks which is being done is given any order that is order matters  in which task being done in the total ways which is being given as that product ? Otherwise if order is being not considered we would have result as $z!*a_{1}*a_{2}..*a_{z}$ as total order ways of tasks doing?
 A: When we talk about product rule ,  we count the number of all possible $\color{blue}{\text{conclusions}}$.Therefore , the number of moves for reaching the conclusion does not matter in product rule. For example , lets think it such that

John have $3$ hats , $5$ trousers , $2$ shirts and $3$ pair of socks. How many possible clothing style can John have ?

In this question ,we look for the conclusions ,i.e , the pictures after John get dressed. Hence , just use product rule (you can also think it like cartesian product).So , $3 \times 5 \times 2 \times 3=90$
However , if you look for the number of ways to reach the conclusion , you should also order your movements to reach final picture.For example , John firsly put on his socks (with $3$ possible choices) , secondly his shirt ($2$ possicle choices) , thirdly his trousers (with $5$ possible choice) , lastly his hats (with $3$ possible choices).You can order these $4$ different cloths types (i.e movements to reach the final picture) by $4!$ ways. Then the answer is $4! \times3 \times 5 \times 2 \times 3=2160$
