How many permutations of the letters DANIEL do not begin with D or do not end with L?
The correct answer is 696.
This answer does not make sense as there are 120 (5!) ways the letters can be arranged so that they start with D, however subtracting this from the total number of permutations, 720 (6!), we get a number less than 696 with only having attempted half the problem!
Any help is much appreciated, thanks in advance.
Best Answer
The requirement "do not begin with D or do not end with L" is a bit tricky, for instance, it means that "DANILE" is accepted. Hence, what is not accepted is of the form "DXXXXL", and therefore we have $6!-4!=696$ possibilities :)