# 5 boya and 3 girls seated in a row.find the probability that all girl sits alternate?

Vaibhav
50 Points
7 years ago
First arrange boys by factorial 5 ways now as □ □ □ □ □ as shown in arrangements there will be 6 blank space then arrange girls by 6C3 ways final answer will be (factorial5 ×6C3)÷factorial8
Piyush Kumar Behera
417 Points
7 years ago
@vaibhav
the above solution is completely wrong,this is for those questions  which give condition that no 2 girls are sitting together,but it is given that all girls are sitting alternate.
for this do the following.Arrange the girls in alternate position    G    G    G  and the girls can be arranged in 3! ways among themselves..
THEN THE FOLLOWING CASES ARE POSSIBLE
B  B  B  G  B  G  B  G  --- girls can be arranged in 3!xboys be arranged in 5! ways
B  B  G  B  G  B  G  B  --- girls can be arranged in 3!xboys be arranged in 5! ways
B  G  B  G  B  G  B  B  --- girls can be arranged in 3!xboys be arranged in 5! ways
G  B  G  B  G  B  B  B  --- girls can be arranged in 3!xboys be arranged in 5! ways

so probability= 4x3!x5!/8!=1/14