There are ten subjects in the school day at St.Vincent’s High School but the sixth standard students have only 5 periods in a day. In how many ways can we form a time table for the day for the sixth standard students if no subject is repeated?a)510b)105c)252d)30240Correct answer is option 'D'. Can you explain this answer?

Question

There are ten subjects in the school day at St.Vincent&#8217;s High School but the sixth standard students have only 5 periods in a day. In how many ways can we form a time table for the day for the sixth standard students if no subject is repeated?a)510b)105c)252d)30240Correct answer is option 'D'. Can you explain this answer?

Answer

Problem Analysis:
We need to find the number of ways to form a time table for the sixth standard students at St. Vincents High School, given that they have only 5 periods in a day and there are 10 subjects in total. We have to ensure that no subject is repeated in the time table.

Solution:
To solve this problem, we can use the concept of permutations.

Step 1: Determine the total number of ways to choose 5 subjects out of 10.
This can be done using the formula for combinations: C(n, r) = n! / (r! * (n-r)!)
In this case, n = 10 (total number of subjects) and r = 5 (number of periods in a day).
So, C(10, 5) = 10! / (5! * (10-5)!) = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1) = 252

Step 2: Once we have chosen the 5 subjects, we need to arrange them in the 5 periods.
This can be done using the concept of permutations. Since the order of subjects matters, we need to find the number of permutations of 5 subjects taken 5 at a time.
This can be calculated using the formula for permutations: P(n, r) = n!
In this case, n = 5 (number of subjects chosen) and r = 5 (number of periods in a day).
So, P(5, 5) = 5!

Step 3: Multiply the results from Step 1 and Step 2 to get the final answer.
Total number of ways = C(10, 5) * P(5, 5) = 252 * 5! = 252 * 5 * 4 * 3 * 2 * 1 = 30240

Therefore, the correct answer is option 'D', 30240.

Answer

The answer should be 252, 10C5

Similar Quant Doubts

There are 2500 students who appeared for an examination. Out of these, 35% students failed in 1 subject and 42% in other subject and 15% of students failed in both the subjects. How many of the students passed in either of the 2 subjects but not in both?

In an examination, 80% students passed in philosophy and 70% students passed in maths. At the same time 15% failed in both the subjects. If390 students passed in both the subjects, how many students appeared in the examination?

In a class of 60 students , 40% of the students passed in Reasoning, 5% of the students failed in Quants and Reasoning, and 20% of the students passed in both the subjects. Find the number of student passed only in reasoning?

In an examination, 42% students failed in Hindi and 52% failed in English. If 17% failed in both the subjects, the percentage of those who passed in both the subject is

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company