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ORGANIZED COUNTING (Additional Practice) 1. 2. 3. 4. 5. Four different math texts and three different English texts are arranged in a row on a shelf. Determine the number of ways the texts can be arranged if: a) the texts are alternated by subject; [144] b) the math texts are grouped together and the English texts are grouped together. [288] Determine the number of ways 8 math teachers can sit around a circular table if: a) Mr. Colavecchio can’t sit beside Mr. Pisocky; [3600] b) Mrs. Peleck must sit across from Ms. DiIorio and Mrs. McCarthy must sit across from Ms. Nestico. [144] Determine the number of arrangements possible using the letters of the word FERMAT if: a) all the letters are used and there are no restrictions; [720] b) all the letters are used and the arrangements must end in a vowel; [240] c) only 5 letters are used; [720] d) only 5 letters are used but the first one must be a T and the arrangement must end in a vowel. [48] Determine the number of 4-digit numbers that can be formed if: a) there are no restrictions; [9000] b) all of the digits are different; [4536] c) all of the digits are different and the number 21 is contained somewhere in the arrangement. [154] Determine the number of odd 4-digit numbers that can be formed using the digits 0 to 8 if there must be a 5 in the number and no digit may be repeated. [636]