Question: Five burglars, A, B, C, D, and E, divide the loot, consisting of five identical gold bars and four identical diamonds. Let Ajk be the

Five burglars, A, B, C, D, and E, divide the loot, consisting of five identical gold bars and four identical diamonds. Let Ajk be the event that A got at least j gold bars and at most k diamonds. Let Bjk, Cjk denote analogous events for burglars B,C (e.g., B21 is the event that B got 2, 3, 4, or 5 gold bars and 0 or 1 diamond). Determine the number x of gold bars and the number y of diamonds received by E if the following events occur (if determination of x and/or y is impossible, give the range of values):

(i) (A20 ∪ B20 ∪ C20) ∩ D30. (ii) Ec 12. (iii) A23 ∩ B13 ∩ C13 ∩ D13. (iv) A23 ∪ B13 ∪

C13 ∪ D13.

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