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Question Number 135181 by liberty last updated on 11/Mar/21

$$\mathrm{A}\mathrm{bag}\mathrm{has}4\mathrm{red}\mathrm{marbles},5\mathrm{white}$$$$\mathrm{marbles},\mathrm{and}6\mathrm{blue}\mathrm{marbles}.\mathrm{Three}$$$$\mathrm{marbles}\mathrm{are}\mathrm{drawn}\mathrm{from}\mathrm{the}\mathrm{bag},(\mathrm{without}$$$$\mathrm{replacement})\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{probability}$$$$\mathrm{that}\mathrm{they}\mathrm{are}\mathrm{all}\mathrm{the}\mathrm{same}\mathrm{color}?$$

Answered by EDWIN88 last updated on 11/Mar/21

$$\mathrm{p}\left(\mathrm{A}\right)=\frac{{\mathrm{C}}_3^4+{\mathrm{C}}_3^5+{\mathrm{C}}_3^6}{{\mathrm{C}}_3^{15}}=\frac{4+10+20}{\left[\frac{15.14.13}{3.2.1}\right]}$$$$=\frac{34}{5.7.13}=\frac{34}{35.13}=\frac{34}{455}$$$$$$

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