Problem

From a club of 19 people, in how many ways can a group of four members be selected to attend a conference?

Solution

Step 1 :This problem is about selecting a group of four members from a club of 19 people. The order in which the members are selected does not matter, so this is a combination problem.

Step 2 :The formula for combination is \(C(n, r) = \frac{n!}{(n-r)! \cdot r!}\), where \(n\) is the total number of items, \(r\) is the number of items to choose, and '!' denotes factorial.

Step 3 :In this case, \(n = 19\) and \(r = 4\).

Step 4 :Substituting these values into the formula, we get \(C(19, 4) = \frac{19!}{(19-4)! \cdot 4!}\).

Step 5 :Calculating this gives a result of 3876.

Step 6 :So, the number of ways a group of four members can be selected from a club of 19 people to attend a conference is \(\boxed{3876}\).

From Solvely APP
Source: https://solvelyapp.com/problems/lBd4h1eLys/

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