A student is allowed to select atmost n books from a collection of (2n + 1) books. If the total number of ways in which he can select books is 63, then n =

The number of ways in which at most n books can be selected out of a collection of (2n + 1) books is 2n+1C1+2n+1C2+…2n+1Cn⇒ 12 2n+1C1+2n+1C1+ 2n+1C2+2n+1C2+……+ 2n+1Cn+2n+1Cn=63⇒ 2n+1C1+2n+1C2n+ 2n+1C2+2n+1C2n−1+……+ 2n+1Cn+2n+1Cn+1=126⇒ 2n+1C1+2n+1C2+…+2n+1C2n=126⇒ 22n+1−2=126⇒ 22n+1=128=27⇒ 2n+1=7⇒ n=3