6 boys and 6 girls sit in a row randomly. find the probability that all the girls sit together
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6 boys and 6 girls sit in a row at random.
Then, the total number of arrangements of 6 boys and 6 girls = arrangement
of 12 people = 12!
When the girls sit together, all 6 girls can be grouped together and regarded
as a single group. Hence we have 6 boys and 1 group of girls = 7 people
Hence, number of arrangements = 7!.
Now these 6 girls can be arranged among themselves = 6!.
The required probability = (6!.7!) /12!
= 1/132
Note guys : (!) - Here stands as factorial. It means ↓↓↓
For example if 4! - it means that the product of numbers below the factor
(i.e) 4! = 4 × 3 × 2 × 1 = 24
_________________________________________________________
☺☺☺ Hope this Helps ☺☺☺
Then, the total number of arrangements of 6 boys and 6 girls = arrangement
of 12 people = 12!
When the girls sit together, all 6 girls can be grouped together and regarded
as a single group. Hence we have 6 boys and 1 group of girls = 7 people
Hence, number of arrangements = 7!.
Now these 6 girls can be arranged among themselves = 6!.
The required probability = (6!.7!) /12!
= 1/132
Note guys : (!) - Here stands as factorial. It means ↓↓↓
For example if 4! - it means that the product of numbers below the factor
(i.e) 4! = 4 × 3 × 2 × 1 = 24
_________________________________________________________
☺☺☺ Hope this Helps ☺☺☺
nitthesh7:
Hey Thank U for the ques as it became my 1000th answer. ☺☺☺
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