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(3)"(-2) Part 2: Calculation and proof questions (80%) Note: About calculation problems and proofs, please elaborate your answers, Points may be deducted you skip too many steps. You should give definitions in details to any symbols or formulas which defined b yourself. If not, you will not get any points. 1. (10%) A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen? (Hint: Represent the books that are chosen by bars and the books not chosen by stars. Count the number of sequences of five bars and seven stars so that no two bars are adjacent) 2. (10%) Let P(n) be the statement that 1 + 2 + ... + n = ?)? for the positive integer w. Show that P(nt) is true for 21