(a(i))[2]
Find how many distinct arrangements can be made from the $12$ letters of the word STRAWBERRIES if there are no restrictions.
(a(ii))[3]
Find how many distinct arrangements there are of the $12$ letters of the word STRAWBERRIES if the $4$ vowels $A, E, E, I$ must all stay together.
(b(i))[2]
$4$ astronauts are selected from a given set of candidates. If the order of selection is ignored, the number of ways the astronauts can be chosen is $3876$. How many ways are there if the order of selection is taken into account?
(b(ii))[2]
$4$ astronauts are selected for a mission. Each astronaut may take $3$ personal possessions with him. How many different ways can the $12$ possessions be arranged in a row if each astronaut’s possessions stay together?