Question

Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.

Options

• `1/2`

• `14/55`

• `2/15`

• `1/3`

Answer 1

`underline(14/55)`

Explanation:

The number of ways to arrange 8 white and 4 black chairs in a row 

= `(12!)/(8! . 4!) = (12 xx 11 xx 10 xx 9)/(4 xx 3 xx 2 xx 1) = 495`

The numbers of blank places between 8 chairs are 7. There is 1 place before the first chair and 1 place after the last chair. Hence, the total number of places is 9.

Hence, 4 black chairs are arranged in these 9 places so that no two black balls are together in `""^9"C"_4 = 126` ways.

So required probability = `126/495 = 14/55`