+2 We are now permanently unable to use the letter A as the starting point. There are four possible routes to the second letter, just like the first, making the total number of routes 44 = 16. But since we can't pick the same letter twice, we have to take away the one possible method of spelling "ARC" (which is right, right, down). Also, since we can't pick the same letter three times, we need to take away the two possible ways of spelling "RHC" (right, down, right, and right, and right, down, right, and right). Last but not least, we can't include the letter combination "RCH," which has only one possible spelling (right, right-down diagonal).flying together
There are a total of 12 different ways to spell "ARCH" using the digits 16121.