Question
Download Solution PDFIn an examination a candidate has to pass in each of the 5 subjects. In how many ways he can fail ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The number of ways to select r things out of n given things wherein r ≤ n is given by:
Calculation:
Given: There are 5 subjects and for a student to pass in an examination the students has to pass in each of the 5 subjects.
Here, we have to find in how many ways a student can fail in the examination.
In order to fail in the examination the student can fail in 1 or 2 or 3 or 4 or 5 subjects out of the 5 subjects in each case.
Case 1: Student fails in any 1 subject out of the 5 subjects.
No. of ways in which student can fail in any 1 subject out of the 5 subjects =
Case 2: Student fails in any 2 subjects out of the 5 subjects.
No. of ways in which student can fail in any 2 subjects out of the 5 subjects =
Case 3: Student fails in any 3 subjects out of the 5 subjects.
No. of ways in which student can fail in any 3 subjects out of the 5 subjects =
Case 4: Student fails in any 4 subjects out of the 5 subjects.
No. of ways in which student can fail in any 4 subjects out of the 5 subjects =
Case 5: Student fails in all 5 subjects.
No. of ways in which student can fail all 5 subjects. =
∴ Total number of ways in which a student can fail in an examination =
Last updated on Jun 18, 2025
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