Question

How many permutations of the word DODATAK

Answer 1

do you know what it would be if the letters were all different?

Answer 2

no

Answer 3

nothing's gonna change

Answer 4

counting principle
if you had 7 different letters there would be
7 choices for the first letter
6 choices for the second
5 for the third
4 for the fourth
3 for the fifth
2 for the sixth
1 for the last one
counting principle says to multiply the number of choices
i.e. \(7\times 6\times 5\times 4\times 3\times 2\times 1=7!\) if they were all different

Answer 5

but here it is a bit different, because you cannot tell the two D apart, and cannot tell the 2 A apart, so the answer is not \(7!\) it is
\[\frac{7!}{2!2!}=\frac{7!}{4}\]

Answer 6

pffff tj wm:DDD you are awesome