There are 7 candidates running for 2 seats on a committee. How many different election results are possible?
15
21
7
42
Assuming the seats are all equivalent,
7C2 = (7*6)/(1*2) = ____
Otherwise, as in maybe president and vice-president, then
7P2 = 7*6 = 42
To determine the number of different election results, you need to calculate the number of ways to select 2 candidates from a total of 7 candidates.
This can be done using the combination formula, which is denoted as "n choose k". In this case, n represents the total number of candidates (7) and k represents the number of candidates to be selected (2).
The formula for combinations is given by:
C(n, k) = n! / (k! * (n-k)!)
Using this formula, we can calculate the number of different election results:
C(7, 2) = 7! / (2! * (7-2)!)
= (7 * 6 * 5!) / (2! * 5!)
= (7 * 6) / 2!
Simplifying further:
= 42 / 2
= 21
Therefore, the number of different election results possible is 21.
The correct answer is 21.
To calculate the number of different election results, we can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r!(n - r)!)
In this case, there are 7 candidates running for 2 seats, which means we want to find C(7, 2).
C(7, 2) = 7! / (2!(7 - 2)!)
= 7! / (2!5!)
= (7 * 6 * 5!) / (2!5!)
= (7 * 6) / (2 * 1)
= 42 / 2
= 21
Therefore, there are 21 different election results possible.