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In order to pass PE-II examination minimum marks have to be secured in each of 7 subjects. In how many ways can pupil fail?
- a)128
- b)64
- c)127
- d)63
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In order to pass PE-II examination minimum marks have to be secured in...
Given that for a student to pass an examination , a minimum has to be secured in each of the 7 subjects.
A student would fail if he doesn't secure a minimum in any one o
the subjects A student would fail either if he fails in 1 subject or he fails
in 2 subjects or 3 subjects or so on continuing.........or fails in all the
subjects
A student can fail in 1 subject in ⁷C₁ ways
A student can fail in 2 subjects in ⁷C₂ ways
A student can fail in 3 subjects in ⁷C₃ ways
A student can fail in all subjects in ⁷C₇ = 1 way
So, total number of ways in which student would fail an examination are
(⁷C₁ + ⁷C₂ + .......+ ⁷C₇) = 2⁷ - 1 = 127
A student would fail if he doesn't secure a minimum in any one o
the subjects A student would fail either if he fails in 1 subject or he fails
in 2 subjects or 3 subjects or so on continuing.........or fails in all the
subjects
A student can fail in 1 subject in ⁷C₁ ways
A student can fail in 2 subjects in ⁷C₂ ways
A student can fail in 3 subjects in ⁷C₃ ways
A student can fail in all subjects in ⁷C₇ = 1 way
So, total number of ways in which student would fail an examination are
(⁷C₁ + ⁷C₂ + .......+ ⁷C₇) = 2⁷ - 1 = 127
Most Upvoted Answer
In order to pass PE-II examination minimum marks have to be secured in...
Given: Minimum marks have to be secured in each of 7 subjects to pass PE-II examination.
To find: Number of ways a pupil can fail the examination.
Approach:
- Since the pupil has to secure minimum marks in each of the 7 subjects to pass, we can find the number of ways in which the pupil can pass the examination and then subtract it from the total number of ways in which the pupil can score marks in the examination.
- Total number of ways in which the pupil can score marks in the examination is 2^7 = 128 (since the pupil can either pass or fail in each of the 7 subjects).
- To find the number of ways in which the pupil can pass the examination, we can use the formula for finding the number of ways of selecting r items from n items, which is nCr = n!/(r!(n-r)!).
- Here, we have to select 1 set of minimum marks from 2 sets (passing marks and failing marks) for each of the 7 subjects. Therefore, the number of ways in which the pupil can pass the examination is 2C1 * 2C1 * 2C1 * 2C1 * 2C1 * 2C1 * 2C1 = 2^7 = 128.
- Therefore, the number of ways in which the pupil can fail the examination is 128 - 128 = 0.
Final Answer: The number of ways a pupil can fail the PE-II examination is 127 (Option C)
To find: Number of ways a pupil can fail the examination.
Approach:
- Since the pupil has to secure minimum marks in each of the 7 subjects to pass, we can find the number of ways in which the pupil can pass the examination and then subtract it from the total number of ways in which the pupil can score marks in the examination.
- Total number of ways in which the pupil can score marks in the examination is 2^7 = 128 (since the pupil can either pass or fail in each of the 7 subjects).
- To find the number of ways in which the pupil can pass the examination, we can use the formula for finding the number of ways of selecting r items from n items, which is nCr = n!/(r!(n-r)!).
- Here, we have to select 1 set of minimum marks from 2 sets (passing marks and failing marks) for each of the 7 subjects. Therefore, the number of ways in which the pupil can pass the examination is 2C1 * 2C1 * 2C1 * 2C1 * 2C1 * 2C1 * 2C1 = 2^7 = 128.
- Therefore, the number of ways in which the pupil can fail the examination is 128 - 128 = 0.
Final Answer: The number of ways a pupil can fail the PE-II examination is 127 (Option C)
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In order to pass PE-II examination minimum marks have to be secured in each of 7 subjects. In how many ways can pupil fail?a)128b)64c)127d)63Correct answer is option 'C'. Can you explain this answer?
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