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marin [14]
3 years ago
5

16. A president and vice-president must be chosen for the executive committee of an organization. There are 17 volunteers from t

he Eastern Division and 24 volunteers from the Western Division. If both officers must come from the same division, in how many ways can the officers be selected?
Mathematics
1 answer:
Ronch [10]3 years ago
7 0

Answer:    412

Step-by-step explanation:

We need to calculate how many different groups of 2 volunteers come out of the 17 volunteers in the Eastern division

C¹⁷₂ = 17!/ 2! (17-2)! ⇒17*16*15!/ 2! * 15! ⇒ C¹⁷₂ = 17*16/2  

C¹⁷₂ = 136

And the same criteria is valid for Western division volunteers

C²⁴₂ = 24!/ 2! *(24-2)! ⇒24*23*22! / 2!*22! ⇒ C²⁴₂ = 24*23/2

C²⁴₂ = 276

And the sum of these two groups will be the total ways the officers can be selected

C = 276 + 136 = 412

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