# Fool's problem of the day, A panel of eight umpires (A, B, C, D, E, F, G and H) is selected for officiating all the Cricket matches played in 2002. The countries which they represent (belong to) are P, Q, R, S, T, U and V, not necessarily in the same order. (i) In the panel, B and D only belong to the same country i.e., T, while the others represent different countries. (ii) A belongs to one of the subcontinent countries i.e., Q or U, while G belongs to the other. (iii) The match between R and V is officiated by E and H. (iv) H is does not belong to country P. Note:- The umpires of the same country as the 2 countries that are playing the match cannot officiate in the match. $$Q_1$$: If a match is played between countries Q and V, then how many different combinations of umpires for that match are possible? $$Q_2$$: If in the above question, it is given that E and H are good friends, and always officiate together in a match, then how many different combinations of umpires are possible for the match between Q and V? Attribution: I faced this question in a selectional test conducted by my coaching institute IMS ( http://www.imsindia.com/ )

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Mathematics