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 $$=$$

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Infinity Learn · Accepted Answer

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

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 =

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