CBSE Class 11-science Answered
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
Asked by Mahesh Padmanabh | 24 Jan, 2011, 08:53: PM
Expert Answer
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.
Answered by | 08 Feb, 2011, 10:24: AM
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