SOLUTION: In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, and the rest are optional. How many arrangements of the subject

Algebra.Com
Question 1173392: In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, and the rest are optional. How many arrangements of the subjects are available for the students?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source): You can put this solution on YOUR website!
Here's how to solve this problem:
**1. Choose the Optional Subjects:**
* Since 4 subjects are core, the students need to choose 3 more subjects from the remaining 10 optional subjects.
* The number of ways to choose 3 optional subjects from 10 is given by the combination formula:
* ¹⁰C₃ = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
**2. Arrange the Chosen Subjects:**
* Once the 7 subjects are chosen (4 core and 3 optional), they can be arranged in 7! ways.
* 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
**3. Calculate the Total Number of Arrangements:**
* To find the total number of arrangements, multiply the number of ways to choose the optional subjects by the number of ways to arrange them:
* Total arrangements = ¹⁰C₃ * 7! = 120 * 5040 = 604800
**Therefore, there are 604,800 possible arrangements of the subjects for the students.**
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
In a school, every grade 10 student need to study 7 subjects out of 14.
It is given that 4 of them are core subject, and the rest are optional.
How many arrangements of the subjects are available for the students?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        Based on the context, my common sense says me that this problem is about combinations,
        and not about permutations, as @CPhill calculates and treats it.

        So, I solve it differently, and my answer is different from that by @CPhill. 


Every student must take 4 core subjects, and a student should take 3 additional subjects, selecting them

from  14-4 = 10 remaining optional subjects.


So, the total number of all possible combinations is   =  = 120.     ANSWER

Solved. The order of subjects in arrangements does not matter.

I am 137% sure that the treatment by @CPhill is not that the problem does require.



RELATED QUESTIONS

In a school, every grade 10 student needs to study 7 subjects out of 14. It is given that (answered by ikleyn)
In a school, every grade 10 students needs to study 7 subjects out of 14. It is given... (answered by ewatrrr)
4. In a certain class there are 21 students in subject A, 17 in subject B and 10 in... (answered by ewatrrr)
Among 18 students in a room, 7 study mathematics, 10 study science, and 10 study computer (answered by ikleyn)
1)IN A CLASS OF 80 STUDENTS 53 STUDY ART,60 STUDY BIOLOGY,36 STUDY ART AND BIOLOGY,34... (answered by solver91311)
You are a principal in a certain school with 30 teachers. Nineteen of them are teaching... (answered by ikleyn)
In a class of 80 students, every student studies Economics or Geography or both. If 65... (answered by Jc0110)
Every student in a school studies either mathematics or physics. Two-thirds of the... (answered by checkley77)
GRAPHICAL ANALYSIS OF DATA 1. The list below shows the ages of the first 20 fans to... (answered by ikleyn)