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Homework Name: Gulnar Alizade Student ID: 202236710102 1. Number of ways 20 people in a list can have 20 different birthdays? Answer: 365! 365 P20 = ———__ (365 — 20)! 2. How many three-letter words can be made using the letters { a, b, c, d, ¢ } ifno repetitions are allowed Answer: Pin, k)= =~ wom POS, 3) = (s23y P(5, 3) =: Ny ! 1 9) — 5x4x3x2x1 PG,3) = PAS, 3) 3. A bakery has 9 different fancy cakes. In how many ways can 5 of the 9 fancy cakes be lined up in a row in the bakery display case’? Answer: P(n, k) = na y — 9x8x7x6x5x4x3x2x1 P(9, 5) ~ 4x3x2x1 PQ,5) =9x8x7x6x5=15,120 4.In how many ways can 3 English, 3 history, and 2 math books be set ona shelf, if the English books are set on the left, history books in the middle, and math books on the right? Answer: English books- 3! History books- 3! Math books- 2! 3!x3!x2!=6x6x2=72 
