"CERTIFICATE" has 11 letters. Since a C must be first, the problem becomes finding the number of distinguishable ways we can follow the C with the 10 other letters. That is the same as the problem: Find the number of distinguishable arrangements of "ERTIFICATE" "ERTIFICATE" has 10 letters, including 2 indistinguishable E's, 2 indistinguishabe T's and 2 indistinguishable I's. We divide 10! by the factorials of all these. Answer:= 453600 Edwin