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LESSON 2 Permutation with Repetition [Distinguishable Permutation] 1 SKILLED BOOK IN MATHEMATICS 10 The number of permutations of n things where a things are alike, b things are alike, c things are alike. I andsoforth,is; P= "' (rtr)! Examples: 1. Find the number of distinguishable permutations of 3. Marvie has 4 blue shirts, 3 white shirts and 2 Red the letters in the word BASKETBALL. shirts. In how many ways can Marvie arrange all her Solutions: n = 10; 23's, 2A's , 2L's shirts in the cabinet? 10! Sclutions:n=9:B=4,W=3,R=2 P: 2!2!2! p_ 9! 10x9x8x7x6x5x4x3x2f _4!3!2! (2x1)(2x1) ! 9x3x7x6x5x4J.' _18144oc _ =A.(3x2x1)(2x1) _ 4 _ 453, 600 ways _ 15 120 12 2. RV have 6 chocolate cakes and 4 Mocha cakes to = 1 250 ways give to 10 teachers. In how many ways can RV distribute the 10 gifts to 10 teachers. Solutions: n =1U;a=6 ,b=4 10! =6!4! 10x9x8x7x6'!' M-x3x2x1 I. Determine the number of permutations of the following words. 1. QUARANTINE - 2. FACEMASK - 3. FACESHIELD - 4. VACCINE - 5. PRONTLINER - ll. Solve the following Permutations. 1. Find the number of distinguishable permutations of the digits of the number 932 539 139. 2. Rhian has 2 beads, 3 red beads, 1 green bead and 1 yellow bead. How many How many different arrangement can be made with the 7 beads if they may be arranged in any linear arrangement. 3. In how many ways can 3 rhinestones, 5 crystals, and 2 precious metals be arranged on a bracelet. 4. In how many ways can 4 Math books, 3 Science books, and 2 English books and 1 Filipino book be arranged on a shelf? 5. Ten volunteers are going to get their meal. In how many ways can the 10 volunteers be arranged in a row in the food station if 4 of them wear green shirts, 3 wear blue shirts, and 3 wear yellow shirts