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In how many ways can we select 5 people from a group of 9 people so that a particular person is never to be included
- a)8C5
- b)9C5
- c)8P5
- d)9P5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In how many ways can we select 5 people from a group of 9 people so th...
Out of 9 people, one has not to be selected.
Therefore, there are total 8 persons. We have to select 5 among them.
Total number of ways = 8C5
Therefore, there are total 8 persons. We have to select 5 among them.
Total number of ways = 8C5
Most Upvoted Answer
In how many ways can we select 5 people from a group of 9 people so th...
To answer these type questions use fomula that
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Community Answer
In how many ways can we select 5 people from a group of 9 people so th...
To solve this problem, we can use the concept of combinations.
Step 1: Understand the problem
We need to select 5 people from a group of 9 people in such a way that a particular person is never included in the selection.
Step 2: Find the total number of ways to select 5 people from a group of 9 people
To find the total number of ways to select 5 people from a group of 9 people, we can use the concept of combinations. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
In this case, we need to select 5 people from a group of 9 people, so n = 9 and r = 5. Substituting these values into the formula, we get:
9C5 = 9! / (5!(9-5)!) = 9! / (5!4!) = (9 * 8 * 7 * 6 * 5!) / (5!4!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126
So, the total number of ways to select 5 people from a group of 9 people is 126.
Step 3: Subtract the number of ways to select 5 people including the particular person
Since we want to exclude a particular person from the selection, we need to subtract the number of ways to select 5 people including that person from the total number of ways to select 5 people.
To select 5 people including the particular person, we have 8 remaining people to choose from (since we have already included one person). So, the number of ways to select 5 people including the particular person is 8C4, which is the number of ways to select 4 people from a group of 8 people.
Using the formula for combinations, we can calculate 8C4 as follows:
8C4 = 8! / (4!(8-4)!) = 8! / (4!4!) = (8 * 7 * 6 * 5!) / (4!4!) = (8 * 7 * 6) / (3 * 2 * 1) = 8 * 7 = 56
Step 4: Calculate the final answer
To find the number of ways to select 5 people from a group of 9 people such that a particular person is never included, we subtract the number of ways to select 5 people including the particular person from the total number of ways to select 5 people.
Total number of ways to select 5 people = 126
Number of ways to select 5 people including the particular person = 56
Number of ways to select 5 people without including the particular person = Total number of ways - Number of ways to select including the particular person
= 126 - 56 = 70
Therefore, the correct answer is option A, 8C5, which represents the number of ways to select 5 people without including the particular person.
Step 1: Understand the problem
We need to select 5 people from a group of 9 people in such a way that a particular person is never included in the selection.
Step 2: Find the total number of ways to select 5 people from a group of 9 people
To find the total number of ways to select 5 people from a group of 9 people, we can use the concept of combinations. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
In this case, we need to select 5 people from a group of 9 people, so n = 9 and r = 5. Substituting these values into the formula, we get:
9C5 = 9! / (5!(9-5)!) = 9! / (5!4!) = (9 * 8 * 7 * 6 * 5!) / (5!4!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126
So, the total number of ways to select 5 people from a group of 9 people is 126.
Step 3: Subtract the number of ways to select 5 people including the particular person
Since we want to exclude a particular person from the selection, we need to subtract the number of ways to select 5 people including that person from the total number of ways to select 5 people.
To select 5 people including the particular person, we have 8 remaining people to choose from (since we have already included one person). So, the number of ways to select 5 people including the particular person is 8C4, which is the number of ways to select 4 people from a group of 8 people.
Using the formula for combinations, we can calculate 8C4 as follows:
8C4 = 8! / (4!(8-4)!) = 8! / (4!4!) = (8 * 7 * 6 * 5!) / (4!4!) = (8 * 7 * 6) / (3 * 2 * 1) = 8 * 7 = 56
Step 4: Calculate the final answer
To find the number of ways to select 5 people from a group of 9 people such that a particular person is never included, we subtract the number of ways to select 5 people including the particular person from the total number of ways to select 5 people.
Total number of ways to select 5 people = 126
Number of ways to select 5 people including the particular person = 56
Number of ways to select 5 people without including the particular person = Total number of ways - Number of ways to select including the particular person
= 126 - 56 = 70
Therefore, the correct answer is option A, 8C5, which represents the number of ways to select 5 people without including the particular person.
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