Solution of question 2 and 3

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{The} \mathrm{are} 10 \mathrm{red} \mathrm{balls} \mathrm{of} \mathrm{different} \mathrm{shades}. \\ \mathrm{First} \mathrm{we} \mathrm{will} \mathrm{arrange} \mathrm{these} 10 \mathrm{balls}. \\ \mathrm{Number} \mathrm{of} \mathrm{ways}=10! \\ \mathrm{Now} \mathrm{after} \mathrm{arrnaging} \mathrm{these} 10 \mathrm{red} \mathrm{balls}, \mathrm{we} \mathrm{will} \mathrm{get} 11 \mathrm{vacant} \mathrm{spaces}. \\ \mathrm{We} \mathrm{have} \mathrm{to} \mathrm{arrange} 9 \mathrm{green} \mathrm{balls} \mathrm{in} \mathrm{these} 11 \mathrm{places}. \\ \mathrm{But} \mathrm{as} \mathrm{these} \mathrm{balls} \mathrm{are} \mathrm{of} \mathrm{idenitcal} \mathrm{shades}, \mathrm{hence} \mathrm{we} \mathrm{just} \mathrm{need} \mathrm{to} \mathrm{select} \\ 9 \mathrm{places} \mathrm{and} \mathrm{need} \mathrm{not} \mathrm{worry} \mathrm{about} \mathrm{arrangements}. \\ \mathrm{Number} \mathrm{of} \mathrm{ways} \mathrm{to} \mathrm{select} 9 \mathrm{places} \mathrm{from} 11{=}^{11}{\mathrm{C}}_9 \\ \mathrm{Hence}: \\ \mathbf{Total}\mathbf{ }\mathbf{ways}\mathbf{=}\mathbf{10}\mathbf{!}{\mathbf{\times }}^{\mathbf{11}}{\mathbf{C}}_{\mathbf{9}} \end{gathered}$$

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