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17. When testing for current in a cable with seven color-coded wires, the author used a...

17. When testing for current in a cable with seven color-coded wires, the author used a meter to test three wires at a time. How many different tests are required for every possible pairing of three ​wires?

The number of tests required is____

18. DNA​ (deoxyribonucleic acid) is made of nucleotides. Each nucleotide can contain any one of these nitrogenous​ bases: A​ (adenine), G​ (guanine), C​ (cytosine), T(thymine). If one of those four bases​ (A, G,​ C, T) must be selected 7 times to form a linear septuplet, how many different septuplets are​possible? All four bases can be selected for each of the seven components of the septuplet.

The number of possible different septuplets is____

19. Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 40 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 46.

Find the probability of winning the jackpot.____

​(Type an integer or simplified​ fraction.)

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