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Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer?
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Panel of 4 doctors 4 officers and one doctor who is also officer how m...
Solution:
To form a committee of 3 members consisting of at least one doctor and one officer, we have to consider the following cases:
Case 1: Committee with 1 doctor and 2 officers
To form this committee, we have to select 1 doctor from the panel of 4 doctors and 2 officers from the panel of 4 officers. The number of ways to select 1 doctor from 4 doctors is 4C1 = 4 and the number of ways to select 2 officers from 4 officers is 4C2 = 6. Therefore, the total number of ways to form this committee is 4 × 6 = 24.
Case 2: Committee with 2 doctors and 1 officer
To form this committee, we have to select 2 doctors from the panel of 4 doctors and 1 officer from the panel of 4 officers. The number of ways to select 2 doctors from 4 doctors is 4C2 = 6 and the number of ways to select 1 officer from 4 officers is 4C1 = 4. Therefore, the total number of ways to form this committee is 6 × 4 = 24.
Case 3: Committee with 3 doctors and no officer
To form this committee, we have to select 3 doctors from the panel of 4 doctors. The number of ways to select 3 doctors from 4 doctors is 4C3 = 4. Therefore, the total number of ways to form this committee is 4.
Total number of committees = number of committees in case 1 + number of committees in case 2 + number of committees in case 3
Total number of committees = 24 + 24 + 4
Total number of committees = 52
Therefore, there are 52 possible committees of 3 members consisting of at least one doctor and one officer.
To form a committee of 3 members consisting of at least one doctor and one officer, we have to consider the following cases:
Case 1: Committee with 1 doctor and 2 officers
To form this committee, we have to select 1 doctor from the panel of 4 doctors and 2 officers from the panel of 4 officers. The number of ways to select 1 doctor from 4 doctors is 4C1 = 4 and the number of ways to select 2 officers from 4 officers is 4C2 = 6. Therefore, the total number of ways to form this committee is 4 × 6 = 24.
Case 2: Committee with 2 doctors and 1 officer
To form this committee, we have to select 2 doctors from the panel of 4 doctors and 1 officer from the panel of 4 officers. The number of ways to select 2 doctors from 4 doctors is 4C2 = 6 and the number of ways to select 1 officer from 4 officers is 4C1 = 4. Therefore, the total number of ways to form this committee is 6 × 4 = 24.
Case 3: Committee with 3 doctors and no officer
To form this committee, we have to select 3 doctors from the panel of 4 doctors. The number of ways to select 3 doctors from 4 doctors is 4C3 = 4. Therefore, the total number of ways to form this committee is 4.
Total number of committees = number of committees in case 1 + number of committees in case 2 + number of committees in case 3
Total number of committees = 24 + 24 + 4
Total number of committees = 52
Therefore, there are 52 possible committees of 3 members consisting of at least one doctor and one officer.
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Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer?
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Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer?.
Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Panel of 4 doctors 4 officers and one doctor who is also officer how many number of committee of 3 cash be made if it has to contain at least one doctor and one officer?.
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