Question

A cupboard contains 3 pink, 3 black and 5 blue shirts well mixed. A person pulls out 2 shirts at random from cupboard. The probability that they match is ______.

Options

• `5/8`

• `16/55`

• `39/55`

• `41/81`

Answer 1

A cupboard contains 3 pink, 3 black and 5 blue shirts well mixed. A person pulls out 2 shirts at random from cupboard. The probability that they match is `16/55`.

Explanation:

 Total no. of ways in which 2 shirts can be drawn out of 11 is ¹¹C₂.

The two shirts match if either they are both pink or they are both black or they are both blue.

So, two matching shirts can be drawn in ³C₂ + ³C₂ + ⁵C₂ ways.

∴ Required probability = `(""^3"C"_2 + ""^3"C"_2 + ""^5"C"_2)/(""^11"C"_2)`

= `(3 + 3 + 10)/55`

= `16/55`