Question

In the intermediate examination, a candidate has to pass in each of the $6$ subjects, then number of ways that he can fail is:

• A. $60$
• B. $61$
• C. $62$
• D. $63$

Answer 1

The correct option is D $63$

In the intermediate examination, a candidate has to pass in each of the $6$ subjects.

Therefore we have $6$ spots to fill with either $P$ or $F$.

If $F$ comes in any of the six places once or more, then he fails.

Total cases can happen: $2^6=64$

Number of cases when he fails no test: $1$

Number of ways in which he can fail: $64-1=63$