Seven students are running for four junior class representative positions in the upcoming student council elections. How many different ways can the students be chosen?
the value is 7 choose 4, or choosing 4 students out of 7 (order does not count).
"7 choose 4" can be evaluated as
7C4 = 7!/((7-4)!4!)
= 7!/(3!4!)
= 5040/(6*24)
= 35
Thank you so much!
To determine the number of different ways the students can be chosen for the four junior class representative positions, we can use the concept of permutations.
In this scenario, we have seven students running for the four positions, and the order in which they are chosen matters (as each position is unique). We can use the formula for permutations to calculate the number of ways:
nPr = n! / (n - r)!
Where "n" is the total number of students and "r" is the number of positions to be filled.
In this case, n = 7 (the total number of students) and r = 4 (the number of positions).
Using the formula, we can calculate:
7P4 = 7! / (7 - 4)!
= 7! / 3!
= (7 × 6 × 5 × 4!) / 3!
= (7 × 6 × 5)
= 210
Therefore, there are 210 different ways the students can be chosen for the four junior class representative positions.