Marks spent half of his weekly allowance on candy. to earn more money his parents let him lead the garden for four dollars. what is his weekly allowance if he ended with $11?

the answer is $14 because 11-4= 7    7*2= 14

you subtract 4 for the extra allowance, and multiply by 2 for the half he spent at the candy store

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."