2022 CJC J2 MYE P2 Q7

Jovan has the following letter cards that are identical except for the printed letters.

These cards are arranged in a row.

1. Find the number of possible arrangements of these cards.[2]
2. Find the number of possible arrangements of these cards, if all the cards of the same letter in either uppercase or lowercase form are grouped together.[3]

Jovan randomly picks \(3\) cards and arranges them in a cardholder that is in the shape of a circle. There are exactly \(3\) slots in the cardholder and each slot of the cardholder can take at most one card.

3. Given that the slots are indistinguishable, find the number of possible arrangements of these cards in the cardholder.[4]