There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?  Choose the correct choice from the following options
A) 43  B) 54  C) 65  D) 91  E) 99
We first count the number of committee in which   (i). Mr. Y is a member   (ii). the ones in which he is not   case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.   Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).   We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.   case (ii): If Mr. Y is not a member then we left with (6+4-1) people.   we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.   Thus, total number of ways is  7+84= 
<gadget id="calculator"> 7+84</gadget>
<output>91</output>
91 ways.   91
<result>D</result>
There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?