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?	Options
A) 45
B) 57
C) 76
D) 91
E) 98
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?