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In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?
- a)30C3
- b)30C4
- c)31C3
- d)31C4
Correct answer is option 'A'. Can you explain this answer?
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In your office 4 posts have fallen vacant. In how many ways a selectio...
Question:
In your office, 4 posts have fallen vacant. In how many ways can a selection be made out of 31 candidates if one candidate is always included?
Solution:
To solve this problem, we can use the concept of combinations. A combination is a way to select items from a larger set without considering the order. In this case, we need to select a team of candidates from a pool of 31, with one candidate always included.
Step 1: Identify the number of candidates to be selected
Since 4 posts have fallen vacant, we need to select 4 candidates from the pool.
Step 2: Identify the number of candidates available
There are a total of 31 candidates available for selection.
Step 3: Identify the number of candidates that must be included
According to the problem, one candidate must always be included in the selection.
Step 4: Calculate the number of ways to select the remaining candidates
To calculate the number of ways to select the remaining candidates, we need to find the combinations of (31-1) candidates taken 3 at a time. This can be represented as ${30 \choose 3}$.
Step 5: Calculate the number of ways to make the selection
Using the formula for combinations, we can calculate ${30 \choose 3}$ as follows:
${30 \choose 3} = \frac{30!}{3!(30-3)!} = \frac{30!}{3! \cdot 27!} = \frac{30 \cdot 29 \cdot 28}{3 \cdot 2 \cdot 1} = 4060$
Therefore, there are 4060 ways to make the selection.
Answer:
The correct answer is option A) 30C3.
In your office, 4 posts have fallen vacant. In how many ways can a selection be made out of 31 candidates if one candidate is always included?
Solution:
To solve this problem, we can use the concept of combinations. A combination is a way to select items from a larger set without considering the order. In this case, we need to select a team of candidates from a pool of 31, with one candidate always included.
Step 1: Identify the number of candidates to be selected
Since 4 posts have fallen vacant, we need to select 4 candidates from the pool.
Step 2: Identify the number of candidates available
There are a total of 31 candidates available for selection.
Step 3: Identify the number of candidates that must be included
According to the problem, one candidate must always be included in the selection.
Step 4: Calculate the number of ways to select the remaining candidates
To calculate the number of ways to select the remaining candidates, we need to find the combinations of (31-1) candidates taken 3 at a time. This can be represented as ${30 \choose 3}$.
Step 5: Calculate the number of ways to make the selection
Using the formula for combinations, we can calculate ${30 \choose 3}$ as follows:
${30 \choose 3} = \frac{30!}{3!(30-3)!} = \frac{30!}{3! \cdot 27!} = \frac{30 \cdot 29 \cdot 28}{3 \cdot 2 \cdot 1} = 4060$
Therefore, there are 4060 ways to make the selection.
Answer:
The correct answer is option A) 30C3.
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In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer?
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