Discrete math PROJECT 1-COUNTING PASSWORDS Choose 6 letters of the English alphabet including all the different characters in your family name. (If you have more than 6 different characters, choose the first 6). Let X be the set of all lower case versions of the letters you have chosen Also let N-(1234.5) and M- (345,67,89). Respond to each of the following requirements. ) Using correct notation, list the elements in the set X. Calculate u N1 and explain how the indusonadson rule works in this case. G0 Write an example of a password consisting of 6 characters with the following properties: The first two characters are selected from set x. The remaining 4 characters are selected from the set N Ga) Let P be the set of all possible passwords constructed according to the rules given in part ) above How many passwords are there in p ? That is, what is In iv) Did you use the product rule or the sum rule to calculate your answer to part pi) Explain your reasoning. (v) Let Q be the set of all possible passwords constructed ording to the rules pvenin part (above tnsthauterennintarastetut How many passwords are there in Q? (v) Use the inclusion/exclusion rule to calculate the number of passwords in PU Q.Explain your reasoning