In an examination, a candidate is required to pass all five different subjects.  The number of ways he can fail is

The candidate will fail if he fails either 1 or 2 or 3 or 4 or 5 subjects

Required number of ways $={}^5{C}_1+{}^5{C}_2+{}^5{C}_3+{}^5{C}_4+{}^5{C}_5$

$=5+10+10+5+1$