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

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