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Sоlve the fоllоwing combinаtorics problems. а) How mаny 6-letter passcode are there if consecutive letters are distinct? Justify your answerb) In how many ways can 4 different twins (8 people in total) can line up so that both twins are next to one another? Justify your answerc) How many 4-digits even numbers with no digit equals 8 are there? Justify your answerd) A class has 10 boys and 12 girls. How many 5 people committees have at least one boy and at least one girl? Justify your answer Note: Write your answers as numerical expressions involving additions, subtractions, multiplications and divisions, or some of them. Do not compute the final numerical answer such that your instructor can identify your reasoning, otherwise, explain in work your answer.