In how many ways can $15$ members of a council sit along a circular table,if the Secretary must sit on one side of the Chairman and the Deputy Secretary on the other side?

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

In how many different ways can the letters of the word '$KURUKSHETRA$' be arranged?

In a certain test,${a_i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, ..., k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?