In how many ways can a student select three couses from seven available courses?
Isn't that just 7 choose 3 ??
Yeah.if we follow the rule of combination the ans comes 35 but the ans is showing 28..but how?
7!/[ 3! * 4! ]
7 * 6 * 5 / 3*2
35 all right
To determine the number of ways a student can select three courses from seven available courses, we can use the concept of combinations.
In this scenario, we need to select three courses out of a total of seven available courses. We can calculate this using the formula for combinations, which is expressed as:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n is the total number of available courses
- r is the number of courses to be selected
Applying this formula to the given scenario, we have n = 7 (seven available courses) and r = 3 (three courses to be selected):
C(7, 3) = 7! / (3! * (7 - 3)!)
Calculating the factorial values:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
Substituting these values into the formula:
C(7, 3) = 5040 / (6 * 24)
= 5040 / 144
= 35
Therefore, there are 35 ways in which a student can select three courses from a set of seven available courses.