answer for clarity

MDM4U1 Unit 1: Permutations 1) Suppose there are nine students that are running for school pupil leader (Braden, Blerton, Christina, Issac, Taylor, Tala, Olga, Hermon, Michael). They each have the opportunity to give a brief speech. How many different orders can they speak in? 2) Madison is trying to choose a new phone number and she needs to choose the last four digits of the number. Her favourite digits are 2, 5, 6, 8, and 9. Each digit can be used at most once. a) How many permutations are there that would include four of her favourite digits? b) How many of these would end with the digit 2? c) How many of these would be odd? 3) How many 5-digit numbers are there that include the digit 5 and exclude the digit 8? 4) A code word is to consist of two distinct English alphabets followed by two distinct numbers from 1 to 9. For example CA 23 is a code word. a) How many such code words are there? b) How many of them end with an even integer? 32!1 5) How many 4-digit numbers are there with distinct digits? 6) How many words can be formed from the letters of the word, TRIANGLE? How many of these begin with T and end with E? 7) How many words can be formed with the letters of the word 'ORDINATE' so that vowels occupy odd places? 8) How many different words can be formed using all the letters of the word MISSISSIPPI? In how many of these permutations do the four 'I's not come together? 9) If all the letters of the word 'AGAIN' are arranged as in a dictionary, what is the fiftieth word? (This is a tricky one!) written in full length? 10) Find the total number of arrangements of the letters in the expression a3 bac*(= aaabbcccc) when Answers: 1) 362880 2) a)120 3) 23816 4) a)46800 5) 4536 6) b) 24 C)48 b)20800 a) 40320 7) 576 8) a)34650 9) NAAIG 10) 1260 b)720 b) 33810