I understand the explanations given above. I want to understand where i m going wrong with my approach.
So, the team need to have 1 PM, 1 TL and 4 Cs. We have 2 PMs, 3 TLs and 7Cs. Of the 7Cs, 2 wont work together.
# of ways in which 1 PM can be chosen: 2 [2C1]
# of ways in which 1 TL can be chosen: 3 [3c1]
# of ways 4 Cs can be chosen: # of ways 5 Cs with no issues can be chosen + # of ways 6 Cs (5 Cs with no issues + 1 of the 2 Cs with issues) can be chosen * 2 (since either 1 of the 2 Cs having issues can be chosen)
--> 5C4 + 6C4*2 = 35
I understand that 35 is also 7C4. However, I am not able to understand how 5C4 + 6C4*2 includes the cases in which the 2 consultants having issues are put in the same team.
Bunuel, It would be very helpful if you could point out where the flaw in my reasoning is. Thanks in advance