A boy has a 1 rupee coin, a 2 rupee coin and a 5 rupee coin in his pocket. He takes out two coins out of his pocket, one after the other.Find the sample space

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Let} \mathrm{Q} \mathrm{denote} \mathrm{a} 1 \mathrm{rupee} \mathrm{coin}, \mathrm{H} \mathrm{denotes} \mathrm{a} 2 \mathrm{rupee} \mathrm{coin} \mathrm{and} \mathrm{R} \mathrm{denotes} \mathrm{a} 5 \mathrm{rupee} \mathrm{coin}. \\ \mathrm{The} \mathrm{first} \mathrm{coin} \mathrm{he} \mathrm{takes} \mathrm{out} \mathrm{of} \mathrm{his} \mathrm{pocket} \mathrm{may} \mathrm{be} \mathrm{any} \mathrm{one} \mathrm{of} \mathrm{the} \mathrm{three} \mathrm{coins} \mathrm{Q}, \mathrm{H} \mathrm{or} \mathrm{R}. \\ \mathrm{Corresponding} \mathrm{to} \mathrm{Q}, \mathrm{the} \mathrm{second} \mathrm{draw} \mathrm{may} \mathrm{be} \mathrm{H} \mathrm{or} \mathrm{R}. \mathrm{So} \mathrm{the} \mathrm{result} \mathrm{of} \mathrm{two} \mathrm{draws} \mathrm{may} \mathrm{be} \mathrm{QH} \mathrm{or} \mathrm{QR}. \\ \mathrm{Similarly}, \mathrm{corresponding} \mathrm{to} \mathrm{H}, \mathrm{the} \mathrm{second} \mathrm{draw} \mathrm{may} \mathrm{be} \mathrm{Q} \mathrm{or} \mathrm{R}. \mathrm{Therefore}, \mathrm{the} \mathrm{outcomes} \mathrm{may} \mathrm{be} \\ \mathrm{HQ} \mathrm{or} \mathrm{HR}.\mathrm{Lastly}, \mathrm{corresponding} \mathrm{to} \mathrm{R}, \mathrm{the} \mathrm{second} \mathrm{draw} \mathrm{may} \mathrm{be} \mathrm{H} \mathrm{or} \mathrm{Q}. \mathrm{So}, \mathrm{the} \mathrm{outcomes} \mathrm{may} \mathrm{be} \mathrm{RH} \mathrm{or} \mathrm{RQ}. \\ \mathbf{Hence}\mathbf{,}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{sample}\mathbf{ }\mathbf{space}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{S}\mathbf{=}\left\{\mathbf{QH}\mathbf{,}\mathbf{ }\mathbf{QR}\mathbf{,}\mathbf{ }\mathbf{HQ}\mathbf{,}\mathbf{ }\mathbf{HR}\mathbf{,}\mathbf{ }\mathbf{RH}\mathbf{,}\mathbf{ }\mathbf{RQ}\right\} \end{gathered}$$

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