(a)[3]
Find the number of distinct arrangements of the $8$ letters in the word KANGAROO in which the two As are adjacent and the two Os are not adjacent.
(b)[2]
A fair $8$-sided dice has faces labelled K, A, N, G, A, R, O, O. The dice is rolled repeatedly. Find the probability that fewer than $6$ rolls of this dice are needed to obtain an A.
(c)[2]
Find the probability that the second A is obtained on the $6$th roll of the dice.