There are 5 bags labeled 1 to 5. All the coins in given bag have the same weight. Some bags have coins of weight 10 gm, other have coins of weight 11 gm. $${\rm I}$$ pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coin is _______ .

In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$.

Which of the following recurrences does $${x_n}$$ satisfy?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$.

The value of $${x_5}$$ is