In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don’t have an office.
The four officers have been selected. Now 2 of the remaining 6 candidates are chosen to be at large board members. In how many ways can they be chosen,
To find the number of ways to choose 2 at-large board members from 6 candidates, we can use the combination formula.
The number of combinations of k items chosen from a set of n items is given by the formula C(n,k) = n! / (k!(n-k)!), where n! represents the factorial of n.
So, in this case, we want to find C(6,2) = 6! / (2!(6-2)!), which is equal to (6*5*4*3*2*1) / ((2*1)(4*3*2*1)).
Simplifying the expression, we get 6*5 / 2*1 = (6*5) / (2*1) = 30 / 2 = 15.
So, there are 15 ways to choose the 2 at-large board members from the remaining 6 candidates.