1.3.7 Five burglars, A , B , C, D , and E, divide the loot, consisting of 5 identical gold bars and 4 identical diamonds. Let A j k be the event that A got at least j gold bars and at most k diamonds. Let Bjkl c j k 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 z of gold bars and the number y of diamonds received by E if the following events occur (if determination of z andor y is impossible, give the range of values): (i) (A20 U B20 U CZOn) 0 3 0 . (ii) E;2. (iii) A23 n B13 nC13n D13.

(iv) A23 u B13 U c13 U 0 1 3 .