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A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. If a particular student is excluded the number of ways in which this can be done is _________.
- a)10C2 x 20C3
- b)9C1 x 20C3
- c)10C2 x 19C3
- d)None
Correct answer is option 'C'. Can you explain this answer?
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A committee is to be formed of 2 teachers and 3 students out of 10 tea...
To solve this problem, we need to use the concept of combinations, specifically the formula for calculating combinations. The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to be selected.
Let's break down the problem step by step:
Step 1: Determine the total number of ways to select 2 teachers from 10 teachers.
We can calculate this using the combination formula:
10C2 = 10! / (2!(10-2)!) = 10! / (2!8!) = (10 * 9) / (2 * 1) = 45
So, there are 45 ways to select 2 teachers from 10 teachers.
Step 2: Determine the total number of ways to select 3 students from 20 students.
Using the combination formula:
20C3 = 20! / (3!(20-3)!) = 20! / (3!17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
So, there are 1140 ways to select 3 students from 20 students.
Step 3: Determine the total number of ways to form the committee without the particular student.
Since the particular student is excluded, we need to calculate the number of ways to select 2 teachers from the remaining 9 teachers and 3 students from the remaining 19 students.
Using the combination formula:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 * 8) / (2 * 1) = 36
19C3 = 19! / (3!(19-3)!) = 19! / (3!16!) = (19 * 18 * 17) / (3 * 2 * 1) = 969
To find the total number of ways to form the committee without the particular student, we multiply the two combinations:
36 * 969 = 34944
Therefore, the correct answer is option 'C' which is 10C2 * 19C3.
nCr = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to be selected.
Let's break down the problem step by step:
Step 1: Determine the total number of ways to select 2 teachers from 10 teachers.
We can calculate this using the combination formula:
10C2 = 10! / (2!(10-2)!) = 10! / (2!8!) = (10 * 9) / (2 * 1) = 45
So, there are 45 ways to select 2 teachers from 10 teachers.
Step 2: Determine the total number of ways to select 3 students from 20 students.
Using the combination formula:
20C3 = 20! / (3!(20-3)!) = 20! / (3!17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
So, there are 1140 ways to select 3 students from 20 students.
Step 3: Determine the total number of ways to form the committee without the particular student.
Since the particular student is excluded, we need to calculate the number of ways to select 2 teachers from the remaining 9 teachers and 3 students from the remaining 19 students.
Using the combination formula:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 * 8) / (2 * 1) = 36
19C3 = 19! / (3!(19-3)!) = 19! / (3!16!) = (19 * 18 * 17) / (3 * 2 * 1) = 969
To find the total number of ways to form the committee without the particular student, we multiply the two combinations:
36 * 969 = 34944
Therefore, the correct answer is option 'C' which is 10C2 * 19C3.
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A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. If a particular student is excluded the number of ways in which this can be done is _________.a)10C2x20C3b)9C1x20C3c)10C2x19C3d)NoneCorrect answer is option 'C'. Can you explain this answer?
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A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. If a particular student is excluded the number of ways in which this can be done is _________.a)10C2x20C3b)9C1x20C3c)10C2x19C3d)NoneCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. If a particular student is excluded the number of ways in which this can be done is _________.a)10C2x20C3b)9C1x20C3c)10C2x19C3d)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. If a particular student is excluded the number of ways in which this can be done is _________.a)10C2x20C3b)9C1x20C3c)10C2x19C3d)NoneCorrect answer is option 'C'. Can you explain this answer?.
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