3 girls and 3 boys
a) Total number of boys and girls is 3+3=6. Thus sample space is 6!=720.
b) Boys and girls alternate: gbgbgb and bgbgbg.
The number of alternate arrangements is the number of possible arrangements of the girls multiplied by the number of possible arrangements of the boys:
P(boys and girls alternate) =
c) Boys sit together; girls sit together: ggggbbb or bbbggg.
Let's consider the group of 3 boys as a single unit and the group of 3 girls as a single unit and arrange everyone accordingly.
The number of arranging 2 units a row is 2!=2.
The number of arranging boys among themselves is 3!=6.
The number of arranging girls among themselves is 3!=6.
Hence the probability is:
P(boys sit together and girls sit together) =
d) Girls sit at the end seats: bbbggg.
The number of arranging boys among themselves is 3!=6.
The number of arranging girls among themselves is 3!=6.
P(girls sit at the end seats) =
e) Millium sits at the left end:
Millium is at the left end so we are left with 5 places and 5 people.
P(Millium sits at the left end) =
Answer:
a) 720
b) 0.1
c) 0.1
d) 0.05
e) 0.1667
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