ABIGAIL Y. DUYOR BSE-ENG 3A PERMUTATION 1. In how many ways can 5 people arrange themselves in a row for picture taking? Solution: n=5 r=5 P(5,5)= 5x4x3x2x1 =120 possible pictures 2. Find the number of permutations of the letters of the word STATISTICS. Solution: There are 10 letters of the word. Assuming that the letters are distinct, there are P(10, 10) = 10! permutations. However, we have to take into consideration that the 3 S’s are alike, the 3 T’s are alike, and the 2 I’s are alike. The permutations of the 3 S’s is P(3, 3) = 3!. The permutations of the 3 T’s is P(3, 3) = 3!. The permutation of the 2 T’s is P(2, 2) = 2! So, we must divide 10! by 3! 3! 2! in order to eliminate the duplicates. Thus, P= 10! 3!3!2! = 10๐ฅ9๐ฅ8๐ฅ7๐ฅ6๐ฅ5๐ฅ4๐ฅ3๐ฅ2๐ฅ1 3๐ฅ2๐ฅ1 3๐ฅ2๐ฅ1 2๐ฅ1 = 3,628,800 72 = 50, 400 permutations COMBINATIONS 1. How many different sets of 5 cards each can be formed from a standard deck of 52 cards? Solution: n=52 r=5 C(n, r) = ๐! ๐!(๐−๐)! = 52! 5!(52−5)! = 52! 5!47! = 52๐ฅ51๐ฅ50๐ฅ49๐ฅ48 5๐ฅ4๐ฅ3๐ฅ2๐ฅ1 = 311,875,200 120 (Cancel the 47! in the 52!) and cancel the 47! in the denominator.) sets of cards = 2,598,960 2. In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve? Solution: n=10 r=5 ABIGAIL Y. DUYOR BSE-ENG 3A ๐! ๐!(๐−๐)! C(n, r)= = 10! 5!(10−5)! 3 2 = 10๐ฅ9๐ฅ8๐ฅ7๐ฅ6๐ฅ5๐ฅ4๐ฅ3๐ฅ2๐ฅ1 5๐ฅ4๐ฅ3๐ฅ2๐ฅ1 = 3x2x7x6 = 252 ways PROBABILITY 1. A survey was conducted to determine girl’s favorite brand of clothes. Each girl chose only one brand from the list of brands Uniqlo, H&M, Shein, Zara or Penshoppe. What is the probability that a girl’s favorite brand is Shein? BRANDS OF CLOTHES NUMBER OF GIRLS UNIQLO H&M SHEIN ZARA PENSHOPPE 10 5 25 13 12 Solution: P(E)= ๐๐ข๐๐๐๐ ๐๐ ๐ค๐๐ฆ๐ ๐กโ๐ ๐๐ฃ๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐ ๐ ๐๐๐๐ ๐๐ข๐ก๐๐๐๐๐ P(Shein)= 25 65 P(Shein)= 25 65 P(Shein)= 5 13 ÷ 5 5 2. Mario has 45 red chips, 12 blue chips, and 24 white chips. What is the probability that Mario randomly selected a red chip? Solution: P(E)= ๐๐ข๐๐๐๐ ๐๐ ๐ค๐๐ฆ๐ ๐กโ๐ ๐๐ฃ๐๐๐ก ๐๐๐ ๐๐๐๐ข๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐ ๐ ๐๐๐๐ ๐๐ข๐ก๐๐๐๐๐ 45 P(Red)= 81 P(Red)= 45 81 P(Red)= 5 9 ÷ 9 9