Question

Three boys and two girls stand in a queue.The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her

Answer 1

I got ans to be 4/5..
It is wrong..
Don't know why is it wrong??
Pls help!

Answer 2

@ganeshie8

Answer 3

is the answer 1/2?

Answer 4

```
BGBGB
GBBGB

BGGBB
GBGBB

GG BBB
```

Answer 5

\[\dfrac{5}{\dbinom{5}{2}}\]

Answer 6

Would you pls listen to my way?

Answer 7

I did it by taking the case when no boy is ahead of girl (any) .
And when exactly one boy is ahead of girl who is having a girl ahead of her
Then i subtracted the probability from 1

Answer 8

I got only three cases for that which are:
GGBBB
BBGBG
BBGGB

Answer 9

Believe me ! I weren't able to make more cases than this..
Pls help

Answer 10

Hey still here ?

Answer 11

Yes!!

Answer 12

R u busy?

Answer 13

Consider a five letter string


_ _ _ _ _

Answer 14

We want to fill that with letters from the set {B, B, B, G, G}

Answer 15

Total how many different strings can you make ?

Answer 16

5C2

Answer 17

Right, lets look at the given constraints

Answer 18

Sure

Answer 19

we have two Girls in the queue

Answer 20

each of them must have at least one more than the number of girls ahead of her

Answer 21

Boy*

Answer 22

can we put a girl at the end of the string ?

Answer 23

Yes

Answer 24

_ _ _ _ G

We cannot put a Girl at the end of the string because, the Girl at the end of the string has 0 boys and 0 girls to the right. Clearly number of boys to the right = number of girls to the right. Violating the given constraint.

Answer 25

We r given that she shud have at least one boy more than no. Of girls ahead her.
So if we fix his position at the end we will get 4 boys ahead of last girl ..
That's our condition also...
What's de fault in that?

Answer 26

Her*

Answer 27

Ahh okay, I have assumed the ahead is to the right

Answer 28

Yeah..that seems fine..

Answer 29

Looks you're assuming the ahead is to the left ?

Answer 30

Yes..
I m assuming girl to be facing towards boys (in front)

Answer 31

Okay lets stick to your convention

Answer 32

Let me rephrase the question accordingly.

Can we put a girl at the front ?
G_ _ _ _

Answer 33

No

Answer 34

Good. No Girl goes at the first position.
Lets see if we can put a Girl at the second postion.

Answer 35

How many different strings are possible with a Girl at the second position honoring the given constraint ?

_ G _ _ _

Answer 36

No

Answer 37

Sorry yes we can do that..

Answer 38

how many and what are they ?

Answer 39

BGBGB

Answer 40

and ?

Answer 41

BGBBG

Answer 42

Two different strings with one Girl at the second position.

Answer 43

Yeah!

Answer 44

Lets put one Girl at the third position.

_ _ G _ _

how many strings are possible ?

Answer 45

Two

Answer 46

BBGBG
BBGGB

Answer 47

Very good! next put one Girl at fourth position

_ _ _ G _

how many strings are possible ?

Answer 48

1

Answer 49

Is BBBGG

Answer 50

so total how many strings honor the given constraint ?

Answer 51

5 ..

Answer 52

Bt sir i had a doubt ..
Did u look at it (in the very first post after u made a reply)?

Answer 53

Oh no sorry
you method looks interesting... let me go through it quick

Answer 54

Sure..i will wait..

Answer 55

Looks you forgot few cases.


No boy is ahead of any girl :
GGBBB

No boy is ahead of first girl :
GBGBB
GBBGB
GBBBG

number of girls = number of boys :
BGGBB

Answer 56

In the case of GBBGB u took two boys ahead of second girl...
How is it possible?

Answer 57

Same with the case GBBBG

Answer 58

U took three boys ahead of last girl..
How can it be possible?

Answer 59

@ganeshie8 pls explain..