8 boys and 2 girls sit in a row randomly. The probability that two girls do not sit together
is
(B)
(C)
(D)
|תם
O
A
O
B
O
с
O
D
6
Answers
Answer:
Total number of boys and girls is 12. Thus sample space is of sitting them random in a row is =12!
Now for favorable event:
8 girls will sit in a row keeping space for one boy in between them,also arrangement will be there, so number of ways in this case will be 8!. And there will be generated 7 place for boys to seat between girls .Now select 4 seat for boys out of 7 and then arrange them, so number of ways of doing this is
7
C
4
×4!=
3!
7!
Hence required probability is =
3!.12!
7!.8!
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Given : 8 B and 2 G sit in a row randomly.
To Find : The probability that two gi rls do not sit together
Solution:
8 B and 2 G
Total = 8 + 2 = 10
Total ways to sit = 10!
Take a case when 2 gi rls sits together
and taking (GG) as one
so Total 9!.2! ways as 2 gi rls can sit in 2!
Hence number of ways two gi rls do not sit together
= 10! - 9!.2!
= 9!(10 - 2)
= 9! 8
The probability that two gi rls do not sit together = 9! 8/10!
= 8/10
= 4/5
The probability that two gi rls do not sit together = 4/5
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