The six letters of the word LONDON are each written on a card and the six cards

Question:

The six letters of the word LONDON are each written on a card and the six cards are then shuffled and placed in a line.

(a) Calculate the number of different arrangements.

(b) Find the probability that the middle two cards both have the letter N on them.

(c) Find the probability that the two cards with letter O are adjacent and the two cards with letter N are also adjacent. The cards are shuffled again and placed in a line, face down. The first two cards in the line are turned over and reveal the letters L. and O.

(d) Find the probability that when the other four cards are turned over the letters will spell LONDON. (L)

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