In an examination, there are 11 papers. A candidate has to pass in at least 6 papers to pass the examination. The number of ways in which the candidate can pass the examination is:

Number of ways passing the examination is S=11C6+11C7+11C8+11C9+11C10+11C11          (1)Using nCr=nCn−r we get S=11C5+11C4+11C3+11C2+11C1+11C0                (2)Adding (1) and (2) we get2S=211⇒S=210