The head of a newly formed government desires to appoint five of the six selected members $P, Q, R, S, T, $and $U$ to portfolios of Home, Power, Defense, Telecom, and Finance. $U$ does not want any portfolio if $S$ gets one of the five. $R$ wants either Home or Finance or no portfolio. $Q$ says that if $S$ gets either Power or Telecom, then she must get the other one. $T$ insists on a portfolio if $P$ gets one.
Which is the valid distribution of portfolios?
- $P$- Home, $Q$ – Power, $R$ – Defense, $S$ – Telecom, $T$ – Finance
- $R$- Home, $S$ – Power, $P$ – Defense, $Q$ – Telecom, $T$ – Finance
- $P$- Home, $Q$ – Power, $T$ – Defense, $S$ – Telecom, $U$ – Finance
- $Q$- Home, $U$ – Power, $T$ – Defense, $R$ – Telecom, $P$ – Finance