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At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]
- a)5040
- b)6210
- c)385
- d)1110
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
At an election , a voter may vote for an y number of candidates, not g...
10C1 + 10C2 + 10C3 + 10C4
= 10 + 45 + 120 + 210 = 385
= 10 + 45 + 120 + 210 = 385
Most Upvoted Answer
At an election , a voter may vote for an y number of candidates, not g...
Given:
- Number of candidates: 10
- Number of candidates to be selected: 4
To find:
Number of ways a voter can vote for at least one candidate
Solution:
To find the number of ways a voter can vote for at least one candidate, we need to consider the different possibilities.
Case 1: The voter votes for only one candidate
In this case, the voter can choose any one candidate from the 10 available candidates. Therefore, the number of ways to vote for only one candidate is 10.
Case 2: The voter votes for exactly two candidates
In this case, the voter can choose any two candidates from the 10 available candidates. The number of ways to select 2 candidates out of 10 is given by the combination formula: C(10, 2) = 10! / (2! * (10-2)!) = 45.
Case 3: The voter votes for exactly three candidates
In this case, the voter can choose any three candidates from the 10 available candidates. The number of ways to select 3 candidates out of 10 is given by the combination formula: C(10, 3) = 10! / (3! * (10-3)!) = 120.
Case 4: The voter votes for all four candidates
In this case, the voter can choose all four candidates from the 10 available candidates. The number of ways to select 4 candidates out of 10 is given by the combination formula: C(10, 4) = 10! / (4! * (10-4)!) = 210.
Total number of ways:
To find the total number of ways a voter can vote for at least one candidate, we add up the number of ways from each case:
Total number of ways = 10 + 45 + 120 + 210 = 385.
Therefore, the correct answer is option C) 385.
- Number of candidates: 10
- Number of candidates to be selected: 4
To find:
Number of ways a voter can vote for at least one candidate
Solution:
To find the number of ways a voter can vote for at least one candidate, we need to consider the different possibilities.
Case 1: The voter votes for only one candidate
In this case, the voter can choose any one candidate from the 10 available candidates. Therefore, the number of ways to vote for only one candidate is 10.
Case 2: The voter votes for exactly two candidates
In this case, the voter can choose any two candidates from the 10 available candidates. The number of ways to select 2 candidates out of 10 is given by the combination formula: C(10, 2) = 10! / (2! * (10-2)!) = 45.
Case 3: The voter votes for exactly three candidates
In this case, the voter can choose any three candidates from the 10 available candidates. The number of ways to select 3 candidates out of 10 is given by the combination formula: C(10, 3) = 10! / (3! * (10-3)!) = 120.
Case 4: The voter votes for all four candidates
In this case, the voter can choose all four candidates from the 10 available candidates. The number of ways to select 4 candidates out of 10 is given by the combination formula: C(10, 4) = 10! / (4! * (10-4)!) = 210.
Total number of ways:
To find the total number of ways a voter can vote for at least one candidate, we add up the number of ways from each case:
Total number of ways = 10 + 45 + 120 + 210 = 385.
Therefore, the correct answer is option C) 385.
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At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer?
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At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer?.
At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer?.
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At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer?, a detailed solution for At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of At an election , a voter may vote for an y number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is [2006]a)5040b)6210c)385d)1110Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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