Step-by-step explanation
This question is actually a problem of permutations and combinations. In option (a) we must the number of possible ways to arrange 2 items from a total of 5 taken order into account. This means that we must give the number of permutations for selecting 2 items out of 5. The number of permutations for selecting k items out of a total of n is given by the following formula:
Here we have n=5 and k=2 so we get:
In option (b) the order doesn't matter. In this case we must give the number of combinations. For a selection of k items out of a total of n the formula for the number of combinations is:
In this case n=5 and k=2 so we get:
Answer
Then the answers are:
(a) 20
(b) 10