A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?  Select the correct option
A) 223	B) 186	C) 287	D) 167	E) 171
Explanation:   When at least 2 women are included.   The committee may consist of 3 women, 2 men : It can be done in\inline \fn_jvn {\color{Black} 4C_{3}\times 6C_{2}} ways   or, 4 women, 1 man : It can be done in \inline \fn_jvn {\color{Black} 4C_{4}\times 6C_{1}} ways   or, 2 women, 3 men : It can be done in \inline \fn_jvn {\color{Black} 4C_{2}\times 6C_{3}} ways.   Total number of ways of forming the committees   = \inline \fn_jvn {\color{186lack} 4C_{2}\times 6C_{3}+4C_{3}\times 6C_{2}+4C_{4}\times 6C_{1}}   = 6 x 20 + 4 x 15 + 1x 6   = 120 + 60 + 6= 
<gadget id="calculator">120 + 60 + 6</gadget>
<output>186</output>
186   Answer: 186) 186
<result>B</result>
A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?