Must appoint 5 different members. There are 17 who are qualified.
How many different ways can they be appointed?
Choose 5 from 17
= C(17,5)
= 17!/(5!12!)
= 6188
To determine the number of different ways that 5 members can be appointed from a pool of 17 qualified candidates, we can use the concept of combinations.
The formula for combinations is nCr = n! / (r!(n-r)!), where n represents the total number of candidates and r represents the number of positions to be filled.
In this case, we have n = 17 (the total number of qualified candidates) and r = 5 (the number of positions to be filled).
Using the formula, we can calculate the number of different ways the 5 members can be appointed:
17C5 = 17! / (5!(17-5)!)
= 17! / (5!12!)
= (17 * 16 * 15 * 14 * 13) / (5 * 4 * 3 * 2 * 1)
= 6188
Therefore, there are 6188 different ways to appoint 5 members from a pool of 17 qualified candidates.