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Consider 11 green balls,9 yellow balls.what is the probability that the 11th ball taken out is a yellow ball?

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11 th ball is yellow

So, 10 ball can select from green,11 th yellow=$_{10}^{10}\textrm{C}$+

       9   "       "    "         "     "     , 1 from yellow and 11 th yellow=$_{9}^{10}\textrm{C}\times_{1}^{9}\textrm{C}$ +

       8  "       "     "        "      "        2 "        "                            =$_{8}^{10}\textrm{C}\times_{2}^{9}\textrm{C}$ +  

............................

       2     "    "           "        "         8  "     "                                =$_{2}^{10}\textrm{C}\times_{8}^{9}\textrm{C}$

So, answer$_{10}^{10}\textrm{C}$+ $_{9}^{10}\textrm{C}\times_{1}^{9}\textrm{C}$ +$_{8}^{10}\textrm{C}\times_{2}^{9}\textrm{C}$ + ................. $_{2}^{10}\textrm{C}\times_{8}^{9}\textrm{C}$=45145
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