The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :

$$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $$ is equal to :