In how many ways can $6$ apples be distributed among $3$ boys,there being no restriction to the number of apples each boy may get?

In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?

All the letters of the word '$EAMCET$' are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

The number of integers between $1$ and $10^{10}$ (inclusive) that contain the digit $1$ is:

$A$ country has $10$ smart cities. The government decides to connect all these cities by road. How many roads does the government need to construct so that every city is connected to every other city?

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?