Question

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colors that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is _____.

Answer 1

Concept:

Suppose we have a string of length n and we want to generate all combinations/permutations taken r at a time with/without repetition, then the possibilities for different cases are given below.

1. Combinations without repetitions = \({n_{{C_r}}}\)

2. Combinations with repetitions = \({\left( {n + r - 1} \right)_{{C_r}}}\)

3. Permutations without repetitions = \({n_{{P_r}}}\)

4. Permutations with repetitions = n^r

Calculation:

In the given question, the total number of colors available (n) = 4

Number colors have taken at a time (r) = 3

Total numbers of cases for picking any three pens are

Total number of combinations = \({\left( {n + r - 1} \right)_{{C_r}}} = {6_{{C_3}}} = 20\)

Number of cases where all three pens have the same color = 4 (all 3 black pens + all 3 blue pen + all 3 green pen + all 3 red pen)

Required probability \(=\frac{4}{20}=0.2\)