2021 DHS J2 MYE Q3 [Modified]

A group of \(10\) people, comprising \(5\) males and \(5\) females, are arranged in a row to hold a long banner for a photo shoot. Find the number of possible arrangements such that

1. at least two females are standing together.[3]
2. exactly two of the five females stand next to each other.[2]

The \(10\) people now proceed to split themselves into groups to head to their dinner venue via cabs.

3. Find the number of ways in which the \(10\) people can be split into two groups of \(3\) each and one group of \(4\).[2]

At the dinner venue, the \(10\) people are directed to a round table with \(12\) chairs.

4. Find the number of ways to seat the \(10\) people at the table.[2]