CAT Exam Model Paper 8 with solutions for free online practice

Case 1: All three balls selected are of the same colour.
The balls selected could be all blue, all white or all black. H ence there are 3 possible colours for selection. Number of ways = ${}_{}^3{\mathit{C}}_1^{}$
Case 2: Exactly two balls selected are of the same colour.
The two same coloured balls selected could either be both red, both blue, both white or both black.
Hence 4 possible colours for selection give ${}_{}^4{\mathit{C}}_1^{}$ ways.
The third ball selected could of any of the remainingthree colours and hence can be selected in ${}_{}^3{\mathit{C}}_1^{}$ ways.
Number of ways ${=}^3{\mathit{C}}_1{.}^4{\mathit{C}}_1$
Total ways = ${}_{}^3{\mathit{C}}_1^{}{+}^3{\mathit{C}}_1{.}^4{\mathit{C}}_1$