You have the assignment of designing color codes for different parts. three colors are used to code on each part. once a combination of three colors is used—such as green, yellow, and red—these three colors cannot be rearranged to use as a code for another part. if there are 35 combinations, how many colors were available?

An assembly consists of two mechanical components. suppose that the probabilities that the first and second components meet specifications are 0.87 and 0.84. assume that the components are independent. determine the probability mass function of the number of components in the assembly that meet specifications. x

Adrawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. what is the least number of socks you must choose, without looking, to be certain that you have chosen two socks of the same colour?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).