Respuesta :
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:
[tex]P=\frac{n!}{(n-k)!}[/tex]Here we have n=5 and k=2 so we get:
[tex]P=\frac{5!}{(5-2)!}=\frac{5!}{3!}=\frac{120}{6}=20[/tex]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:
[tex]C=\frac{n!}{(n-k)!k!}[/tex]In this case n=5 and k=2 so we get:
[tex]C=\frac{5!}{(5-2)!2!}=\frac{5!}{3!2!}=\frac{120}{6\cdot2}=\frac{120}{12}=10[/tex]AnswerThen the answers are:
(a) 20
(b) 10
