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Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee?
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Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In ho...
**Problem:**
Out of 6 teachers and 4 boys, a committee of 8 is to be formed. In how many ways can this be done when there should not be less than four teachers in the committee?
**Solution:**
To solve this problem, we need to use the concept of combinations.
**Step 1:** Determine the number of ways to select 4 or more teachers from the 6 teachers.
- We can select 4 teachers from 6 in C(6,4) ways.
- We can select 5 teachers from 6 in C(6,5) ways.
- We can select 6 teachers from 6 in C(6,6) ways.
**Step 2:** Determine the number of ways to select the remaining members of the committee.
- We need to select 4 members from the remaining 8 (4 boys and the selected teachers) in C(8,4) ways.
**Step 3:** Multiply the results from Step 1 and Step 2 to get the total number of ways to form the committee.
- For each case in Step 1, we have C(8,4) ways to select the remaining members.
- Therefore, the total number of ways to form the committee is:
C(6,4) * C(8,4) + C(6,5) * C(8,3) + C(6,6) * C(8,2)
**Step 4:** Simplify the result.
- C(6,4) = 15
- C(6,5) = 6
- C(6,6) = 1
- C(8,4) = 70
- C(8,3) = 56
- C(8,2) = 28
- Therefore, the total number of ways to form the committee is:
15 * 70 + 6 * 56 + 1 * 28 = 1186
**Answer:**
There are 1186 ways to form the committee with at least 4 teachers.
Out of 6 teachers and 4 boys, a committee of 8 is to be formed. In how many ways can this be done when there should not be less than four teachers in the committee?
**Solution:**
To solve this problem, we need to use the concept of combinations.
**Step 1:** Determine the number of ways to select 4 or more teachers from the 6 teachers.
- We can select 4 teachers from 6 in C(6,4) ways.
- We can select 5 teachers from 6 in C(6,5) ways.
- We can select 6 teachers from 6 in C(6,6) ways.
**Step 2:** Determine the number of ways to select the remaining members of the committee.
- We need to select 4 members from the remaining 8 (4 boys and the selected teachers) in C(8,4) ways.
**Step 3:** Multiply the results from Step 1 and Step 2 to get the total number of ways to form the committee.
- For each case in Step 1, we have C(8,4) ways to select the remaining members.
- Therefore, the total number of ways to form the committee is:
C(6,4) * C(8,4) + C(6,5) * C(8,3) + C(6,6) * C(8,2)
**Step 4:** Simplify the result.
- C(6,4) = 15
- C(6,5) = 6
- C(6,6) = 1
- C(8,4) = 70
- C(8,3) = 56
- C(8,2) = 28
- Therefore, the total number of ways to form the committee is:
15 * 70 + 6 * 56 + 1 * 28 = 1186
**Answer:**
There are 1186 ways to form the committee with at least 4 teachers.
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Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee?
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Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee? 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 Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee?.
Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee? 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 Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of 6 teachers and 4 boys, a committee of 8 is to be formed . In how many ways can this be done when there should not be less than four teachers in the committee?.
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