The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

The largest value of $n$, for which $40^n$ divides $60!$, is

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

The largest $n \in \mathbb{N}$, for which $7^n$ divides $101!$, is :