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The office staff of XYZ Corporation presently consists of three bookkeepers, P, Q, R and 5 secretaries
S, T, U, V, W. The management is planning to open a new office in another city using 2 bookkeepers
and 3 secretaries of the present staff. To do so they plan to separate certain individuals who don‟t
function well together. The following guidelines were established to set up the new office:
(i) Bookkeepers P and R are constantly finding fault with one another and should not be sent
together to the new office as a team.
(ii) R and T function well alone but not as a team, they should be separated.
(iii) S and V have not been on speaking terms and shouldn‟t go together.
(iv) Since S and U have been competing for promotion they shouldn‟t be a team. 

If $R$ and $U$ are moved to the new office, how many combinations are possible?






Solution

If $R$ is selected, then $P$ and $T$ cannot go. So the second bookkeeper must be $Q$. Secretaries already include $U$. Remaining two must be chosen from $S, V, W$ such that $S$ and $U$ cannot go together → $S$ is excluded Possible pairs: $(V, W)$ only So only one valid combination exists.


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