Final answer:
The number of ways the students can be chosen for the positions of President, Vice President, Treasurer, and Secretary is 72,240.
Step-by-step explanation:
To find the number of ways the students can be chosen for the positions of President, Vice President, Treasurer, and Secretary, we can use the concept of permutations. Since each position can only be filled by one student, we need to find the number of different arrangements of the 21 students for the 4 positions. The number of ways to arrange the students is given by the formula:
Number of arrangements = nPr = n! / (n-r)!
where n is the total number of students (21) and r is the number of positions (4).
Substituting the values, we get:
Number of arrangements = 21P4 = 21! / (21-4)! = 21 x 20 x 19 x 18 = 72,240