Total candidate = 22
Politicians =5 Business men =6
Question=. If the list includes candidates from at least four professions and no two member of the discussion panel are to be of the same profession, then in how many ways can the panel be constituted?
Statement 1
The list includes 5 journalist and two Authors
Politician +Businessmen+Author+Journalist=Total Candidates
5+6+5+2=18
From the question stem; Total candidates is supposed to be 22, so there are 22-18=4 candidates that are unaccounted for , Statement 1 is INSUFFICIENT.
Statement 2
The list include only one professional from which there are fewer than 3 candidates , this means that there is only one professional from which there are fewer than three candidates
This means that there is only one profession that has less three Candidates. This information does not tell us about less than 3 Candidates.This information does not tell us about the total number of profession . So number of ways in which panel can be constituted is unknown. Statement 2 is NOT SUFFICIENT.
Combining both statement 1 and 2 together
Politicians = 5 , Business men= 6 , Journalist=5 Authors = 6
The Author profession account s for the profession that has less than two candidates so there is now 5+6+5+2=18 Candidates.
, for the remaining four candidates there is no way to divide them into separate profession because only one profession is allowed to have less than 3 candidates and that has been taken up by the Author
So there are four known profession and 1 unknown profession
Total profession = 5
No of way to select four distinct member from this 5 profession
$$5C_4=\frac{5!}{4!\left(5-4\right)!}=\frac{5!}{4!\cdot1!}=\frac{5\cdot4\cdot3\cdot2\cdot1}{4\cdot3\cdot2\cdot1\cdot1}=5$$
Both statement combined together are SUFFICIENT.
$$answer\ is\ Option\ C$$
