Discrete math PROJECT 1-COUNTING PASSWORDS Choose 6 letters of the English alphabet including all the different characters in your fame (If you have more than 6 different char the first 6). Let X be the set of all lower case versions of the letters you have chosen. Also let N-(1.2.34.5) and M -(3,45,6789). Respond to each of the folowing requirements acters, choose in the set X.CalculateX U NI and explain how the inlusion/exdlusion rule works in this case i 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 (a) Let P be the set of all possible passwords constructed according to the rules given in part (i) above How many passwords are there in P ? That is, what is IPl? v) Did you use the product rule or the sum rule to cakculate your answer to part a).Explain your reasoning v) Let Q be the set of all possible passwords constructed according to the rules given in part (il) above except that the remaining 4 characters are How many passwords are there in Q? v) Use the inclusion/exdlusion rule to calculate the number of passwords in PUQ.Explain your reasoning