2025 HCI P2 Q5

The eleven letters in the word INSPIRATION are each printed on separate, identical cards.

1. Find the number of ways in which the cards can be arranged in a row if,
   1. there are no restrictions,[1]
   2. the letters N are together or the letters I must all be separated, but not both.[3]
2. Three of the eleven cards are removed at random. Find the probability that the letters on the eight cards left behind are all distinct.[2]