Question

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

Options

• `1/21`

• `4/7`

• `2/7`

• `5/7`

Answer 1

`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`.