Question

Cancidates were asked to come to an interview with 3 pens each. Black, Blue, greena nd red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is .

• A. 0.2

Answer 1

The correct option is A 0.2

The number of ways of selecting 3 pens of same colour is
${}^4{C}_1=4$

The number of ways of selecting 3 pens of two different colours $={}^4{C}_2\times {}^2{C}_1=12$

$[\because$ 3rd pen can be selected only by one of these two selected colors that's why we have multiplied with ${}^2{C}_1]$.

The number of ways of selecting 3 pens of three different colours $={}^4{C}_3=4$

Total number of ways $={}^4{C}_1+{}^4{C}_2\times {}^2{C}_1+{}^4{C}_3$

$=4+12+4=20$

Favourable cases $={}^4{C}_1=4$

$p\left(E\right)=\frac{4}{20}=\frac{1}{5}=0.2$