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The presidents, vice presidents, and secretary-treasurers from each of four classes are eligible for an all-school council. How many ways can four officers be chosen from these representatives? How many ways can they be chosen if the president must be selected from the sitting presidents, the vice president from the sitting vice presidents, the secretary from the sitting secretary-treasurers, and the treasurer from everybody who’s left? |
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Answer» Given : The PRESIDENTS, vice presidents, and secretary-treasurers from each of four classes are eligible for an all-school council. How many ways can four officers be chosen from these representatives To find : How many ways can four officers be chosen from these representatives Solution: The presidents, vice presidents, and secretary-treasurers from each of four classes 4 Presidents , 4 vice presidents , 4 Secretary , 4 Treasures HENCE Total = 4 * 4 = 16 four officers be chosen from these representatives = ¹⁶C₄ = 1820 ways 2nd case : president must be selected from the sitting presidents = ⁴C₁ = 4 ways vice president must be selected from the sitting vice presidents = ⁴C₁ = 4 ways the secretary from the sitting secretary-treasurers = ⁸C₁ = 8 ways 3 PEOPLE Selected so remaining = 16 -3 = 3 treasurer can be selected in 13 Ways Total Ways = 4 * 4 * 8 * 13 = 1664 1664 Ways they can be chosen Learn More: a group consists of 7 boys and 5 girls find the number of ways in ... IN HOW MANY WAYS, WE CAN CHOOSE TWO TEAMS OF MIXED ... in how many different ways can you cricket team finish the trophy ... |
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