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
(i)
at least two females are standing together.
[3]
(ii)
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.
(iii)
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.
(iv)
Find the number of ways to seat the $10$ people at the table.
[2]
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