a bag contains 6 red , 5 white and 4 black balls . 2 balls are drawn .find the probability that non of them is red.

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{A} \mathrm{bag} \mathrm{contains} 6\mathrm{red},5\mathrm{white},4\mathrm{black} \\ 2 \mathrm{balls} \mathrm{are} \mathrm{drawn} \\ \mathrm{Probability} \mathrm{that} \mathrm{non} \mathrm{of} \mathrm{them} \mathrm{is} \mathrm{red}=\frac{{}^9\mathrm{C}_2}{{}^{15}\mathrm{C}_2}=\frac{\mathrm{Two} \mathrm{balls} \mathrm{drawn} \mathrm{from} 5\mathrm{white} +4 \mathrm{black}}{\mathrm{total}} \\ \mathrm{P}=\frac{{\displaystyle \frac{9!}{\left(2!\right)\left(7!\right)}}}{{\displaystyle \frac{15!}{\left(2!\right)\left(13!\right)}}}=\frac{36}{105}=0.34 \left(\mathrm{Answer}\right) \end{gathered}$$

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