Arestaurant makes a special citrus dressing for its salads. here is how the ingredients are mixed:

1/3 is oil 1/4 is orange juice

1/6 is vinegar 1/4 is lemon juice

when the ingredients are mixed in the same ratio as shown above, every batch of dressing tastes the same. study the measurements for each batch in the table. fill in the blanks so that every batch will taste the same. ! i will give you ↓14 points↑·⇔⇒≅≡

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."