Question
Mon January 24, 2011 By: Mahesh Padmanabh

A student is allowed to select at most n books from a collection of (2n+1) books .If the total number of ways in which he can select at least one book is 63. Find the value of n

Expert Reply
Tue February 08, 2011
Dear Student,
Here is the solution:
 
Since the student is allowed to select at the most n-books out of (2n + 1) books, therefore, he can choose, one book, two books or at the most n books. The number of ways of selecting at least one books are

        2n+1C1 + 2n+1C2 + ......... 2n+1Cn = 63 = S (Say)

Again, we know that

        2n+1C0 + 2n+1C1 + ......... 2n+1Cn + 2n+1C2n+1 = 22n+1

Now  2n+1C0 = 2n+1C2n+1 = 1

        2n+1C1 = 2n+1C2n etc.........

Hence, we have

        1 + 1 + 2S = 22n+1

or     2 + 2 x 63 = 22n+1

or     128 = 22n+1 or 27 = 22n+1

=>     2n+1 = 7

or     2n = 6

        n = 3

 

 

Regards
Team Topperlearning.
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