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At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these?
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At an election there are 5 candidates and 3 members are to be elected....
Solution:
Given, there are 5 candidates and 3 members are to be elected.
To find: The number of ways a voter can choose to vote.
Approach:
For each candidate, a voter has two choices - either to vote or not to vote.
For 3 members to be elected, a voter can vote for any number of candidates from 0 to 3.
Therefore, the total number of ways a voter can choose to vote is given by the sum of the binomial coefficients of (5,0), (5,1), (5,2), and (5,3).
Calculation:
- (5,0) = 1
- (5,1) = 5
- (5,2) = 10
- (5,3) = 10
Total number of ways = (5,0) + (5,1) + (5,2) + (5,3) = 1 + 5 + 10 + 10 = 26
But, the voter cannot choose to vote for more than 3 candidates, so we need to subtract the case where the voter chooses to vote for all 5 candidates.
Number of ways where the voter chooses to vote for all 5 candidates = (5,3) = 10
Therefore, the actual number of ways a voter can choose to vote is 26 - 10 = 16.
Hence, option (d) none of these is the correct answer.
Final Answer: (d) none of these.
Given, there are 5 candidates and 3 members are to be elected.
To find: The number of ways a voter can choose to vote.
Approach:
For each candidate, a voter has two choices - either to vote or not to vote.
For 3 members to be elected, a voter can vote for any number of candidates from 0 to 3.
Therefore, the total number of ways a voter can choose to vote is given by the sum of the binomial coefficients of (5,0), (5,1), (5,2), and (5,3).
Calculation:
- (5,0) = 1
- (5,1) = 5
- (5,2) = 10
- (5,3) = 10
Total number of ways = (5,0) + (5,1) + (5,2) + (5,3) = 1 + 5 + 10 + 10 = 26
But, the voter cannot choose to vote for more than 3 candidates, so we need to subtract the case where the voter chooses to vote for all 5 candidates.
Number of ways where the voter chooses to vote for all 5 candidates = (5,3) = 10
Therefore, the actual number of ways a voter can choose to vote is 26 - 10 = 16.
Hence, option (d) none of these is the correct answer.
Final Answer: (d) none of these.
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At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these?
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At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these? 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 At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these?.
At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these? 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 At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is (a) 20 (b) 22 (c) 25 (d) none of these?.
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