6. Recall that if you have a collection consists of n objects of which:
n1 are of type 1 and are indistinguishable from
each other;
n2 are of type 2 and are
indistinguishable from each other;
:
:
nk are of type k and are indistinguishable from
each other;
and n1 + n2 + ... + nk = n. Then the number
of distinct permutations of the n objects is n! / (n1!
n2! ... nk!).
In the word abracadabra, there are 5 a's, 2 b's, 1 c, 1 d and 2 r's. So there are 11! / (5! 2! 1! 1! 2!) = 83160 distinct permutations of the letters.