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प्रश्न
Select the correct option from the given alternatives :
There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is
विकल्प
`1/21`
`4/7`
`2/7`
`5/7`
उत्तर
`5/7`
Explanation;
There are 5 girls and 2 boys. They can be arranged among themselves in 7P7 = 7! ways.
∴ Girls can be arranged among themselves in 5P5 = 5! ways.
No two boys should sit together
Let girls be denoted by letter G.
– G – G – G – G – G–
There are 6 places, marked by ‘__’ where boys can sit.
∴ Boys can be arranged in 6P2 = `(6!)/((6 - 2)!`
= `(6 xx 5 xx 4!)/(4!)`
= 30 ways.
∴ Required probability = `(5! xx 30)/(7!)`
= `(5! xx 30)/(7 xx 6 xx 5!)`
= `5/7`.
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