Question

In a library there are n different books on mathematics and one can draw any number of books.If the number of ways in which the books can be drawn is 4095,then

Answer 1

Given: In a library there are n different books on mathematics and one can draw any number of books.

To find: If the number of ways in which the books can be drawn is 4095, then n = ?

Solution:

• Now we have given the number of ways in which the books can be drawn is 4095, so:

                nC1 + nC2 + nC3 + ................. + nCn = 4095

• The general term will be:

                2^n - 1 = 4095

                2^n = 4095 + 1

                2^n = 4096

• Now factors for 4096 are:

                4096 = 2 x 2 x ....... x 2 (12 times)

                2^n = 2^12

                n = 12

Answer:

           So the value of n is 12.