Let C be the collection of all possible arrangements of the

Let C be the collection of all possible arrangements of the letters m,a,r, and y (so ryam is a valid arrangement, but mrmy is not, because it uses the m twice). Part a: List all elements of C. Part b: Let S1 be the event that the last letter of an arrangement is y, and S2 be the event that the first letter of an arrangement is m. Of the elements in your list from part a, which are in S1 S2? Part c: Let S1 and S2 be as in part b. Of the elements in your list from part a, which are in S1 S2?

Solution

a)

mary
mayr
mray
mrya
myar
myra
amry
amyr
army
arym
aymr
ayrm
rmay
rmya
ramy
raym
ryma
ryam
ymar
ymra
yamr
yarm
yrma
yram

b)S1 intersection S2

mary
mray

c) S1 union S2

mary
mray
mayr
mrya
myar
myra
amry
army
rmay
ramy