Let's play with the word: ANTANANARIVO.

(a). What is it? If you do not know, Google it.
(b). In how many distinct ways can the letters of this word be rearranged. You must set up the numerical expression and then evaluate it.
(c). What is the probability that such a random rearrangement starts with all four A's as the first four letters? You must setup the numerical expression and then simplify it.

Abilliard ball is struck by a cue. it travels 1 0 0 cm 100cm before ricocheting off a rail and traveling another 1 2 0 cm 120cm into a corner pocket. the angle between the path as the ball approaches the rail and the path after it strikes the rail is 4 5 ∘ 45 ∘ . how far is the corner pocket from where the cue initially struck the ball? do not round during your calculations. round your final answer to the nearest centimeter.