Solve wolf, goat and cabbage problem $[3$pts$].$ A farmer went to a market and purchased a wolf,

a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a

boat. But crossing the river by boat, the farmer could carry only himself and a single one of his

purchases: the wolf, the goat, or the cabbage. However, if left unattended together, the wolf

would eat the goat, or the goat would eat the cabbage. The farmer's challenge was to carry

himself and his purchases to the far bank of the river, leaving each purchase intact.

a$.$ How many legal states of the puzzle there are $(1$pt$)$

i$.3$

ii$.2$

iii. $6$

iv$.7$

v$.12$

vi$.8$

vii. $10$

viii. $9$

ix$.16$

x$.$ None of the above