2021 JPJC J2 MYE P2 Q10
In a certain Junior College, each class is assigned to one of the four Houses. The Captain, the Vice-Captain and the Secretary are the leaders of each House. The leaders of the four Houses meet for their annual meeting. Before the start of the meeting, they want to take a group photo on a flight of stairs. Due to safe management measures, they can only stand on the first, fourth and seventh step, with four leaders in a row on each step.
Find the number of ways that they can stand to take the photo if
(i)
there are no restrictions,
[1]
(ii)
each row has a leader from each House.
[3]
At the meeting, they want to form a working team of $5$ leaders for a sports event.
(iii)
Find the number of ways this can be done if each House has at least $1$ representative.
[3]
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