The group U(14) has: اختر احدى الجابات only 2 subgroups 4 sub groups 7 subgroups 6 sub groups

2. A survey states whether a household income (inc) is high or low based on the make of the cars the husband and wife each own. There are 4 car types, dom(h) = dom(w) = {/1234}, the first two being 'cheap' and the last two being 'expensive'. The survey finds that, given their household income, the types of cars owned by a husband and wife are independent ie. wife's car type I husband's car type family income and the following probabilities p(inc = louw) = 0.8, p(wline low)= [0.7 0.30 0", p(wlinc= high) = [0.2 0.1 0.40.3", p(hline = low) = [0.2 0.8 0 0 and p(h|ine = high) = [000.30.7" Compute the marginal p(w,h) and show that whilst hlwine, it is not the case that hLw.

1) Let Pn denote the number of ways to build a pipe n units long, using segments that are either plastic or metal, and (for each material) come in lengths of 1 unit or 2 units. For example, p1 = 2 since we can use a 1-unit segment that is either plastic or metal, and p2= 6 since we can use either type of 2-unit segment, or any of the 22 possible ordered choices of 2 segments each having a length of 1 unit. Define po = 1. Determine a recurrence relation for pn. Give a combinatorial proof that your recurrence relation does solve this counting problem. Use your recurrence relation and the method of generating functions to find a formula for pn. [Hint: Your final answer should be Pn= 1 2√3 (1+√3)+¹-(1-√3)+¹ for every n 20.] 2) Let s, denote the number of lists of any length that have the fixed sum of n, and whose entries come from {1,2,3). For example, s2 = 2 because (1,1) and (2) are the only such lists; and 84 = 7 because the lists are (3, 1), (1, 3), (2, 2), (2, 1, 1), (1, 2, 1), (1, 1,…

The rooms in a house are adjacent as indicated in the following table. An '*' means they are adjacent, and a '-'means they are not. Rm KLMNOPQRSTU K L M ZOPORST اد. T U How few colors can be used so that each room is painted a color so in which no two adjacent rooms are the same color? List the rooms in groups with the same color, with the groups separated by semicolons (i.e. F E; A; G B D; C).