<p>Math 103 - Cooley Statistics for Teachers OCC</p><p>Activity #18 – Permutations</p><p>California State Content Standard - Statistics, Data Analysis, and Probability N/A</p><p>Def – Number of Permutations The number of permutations of n distinct items is n factorial, symbolized n!, where n! n(n 1)(n  2)   (3)(2)(1)</p><p>Permutation Formula The number of possible permutations (ordered arrangements) of r objects from a collection of n objects is given by the formula: n! P = P( n , r )= n r (n  r)! Permutations of Duplicate Objects</p><p>The number of distinct permutations of n objects where r1 of the objects are identical, r2 of the objects are n! identical,….., rk of the objects are identical is found by the formula: r1!r2!rk !</p><p> Exercises:</p><p>5! 7! 1) 7! 2) 3) 4) P(9,3) 5) P(8,2) 3! 4!</p><p>6) In how many ways can 8 CD’s be arranged on a shelf? </p><p>7) How many different five letter words can be made from the letters of SWING if there are to be no repetitions of letters?</p><p>8) If a softball league has 10 teams, how many different end of the season rankings are possible? (Assume no ties). </p><p>9) In how many ways can a sorority of 20 members select a president, vice president and treasury, assuming that the same person cannot hold more than one office.</p><p>10) How many different arrangements can be made using two of the letters of the word TEXAS if no letter is to be used more than once?</p><p>11) A key pad lock has 10 different digits, and a sequence of 4 different digits must be selected for the lock to open. How many key pad codes are possible?</p><p>12) In how many different ways can the letters of the word “MISSISSIPPI” be arranged?</p><p>13) In how many different ways can the letters of the word “TOYOTA” be arranged?</p><p>14) In how many different ways can the letters of the word “BOOKKEEPER” be arranged?</p><p>15) A music teacher selects 4 boys and 5 girls to sing at a PTA meeting. The children stand in a row with the boys on the left and the girls on the right. How many such arrangements of children are possible if the teacher can select from seven boys and nine girls?</p>