in an election 3 persons are to be elected from 6 candidates.A voter can cast an number of votes but not more than the candidates to be elected in how many was can he cast his vote

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{As} \mathrm{three} \mathrm{persons} \mathrm{are} \mathrm{to} \mathrm{be} \mathrm{selected} \mathrm{out} \mathrm{of} \mathrm{six}, \mathrm{hence} \mathrm{a} \mathrm{person} \mathrm{can} \mathrm{cast} 3 \mathrm{votes} \mathrm{at} \mathrm{maximum}. \\ \mathrm{Total} \mathrm{ways}= \mathrm{Number} \mathrm{of} \mathrm{ways} \mathrm{to} \mathrm{cast} \left(\mathrm{One} \mathrm{vote} \mathrm{OR} \mathrm{Two} \mathrm{votes} \mathrm{OR} \mathrm{Three} \mathrm{votes}\right) \\ {=}^6{\mathrm{C}}_1{+}^6{\mathrm{C}}_2{+}^6{\mathrm{C}}_3 \\ =6+\frac{6\times 5}{2\times 1}+\frac{6\times 5\times 4}{3\times 2\times 1} \\ =6+15+20 \\ \mathbf{\Rightarrow }\mathbf{Total}\mathbf{ }\mathbf{ways}\mathbf{=}\mathbf{ }\mathbf{41}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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