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?
Answers
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
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