Because of declining profits, corporate headquarters at Jaguar Motor Industries

Question

Because of declining profits, corporate headquarters at Jaguar Motor Industries has decided to keep only 5 of its 8 existing auto assembly plants open after winter 2018. How many groupings of the five plants to remain open are possible? (Hint: Does order matter?) Show Work

A Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief marketing officer. There are 13 qualified candidates. How many different ways can the 4 officers be appointed?   (Hint: Does order matter?) Show Work

Explanation / Answer

(1) Total number of industries = 8

Number of industries which will be opened after 2018 = 5

So, number of groupings = 8C5 = 8!/(5!*3!) = 56.

(2) Total number of candidates = 13

Required number of officers = 4

So, Number of ways selecting them are = 13C4 = 13!/(4!*9!) = 715

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