SOLUTION: find the number of arrangement of the letters of the word CERTIFICATE which begins with c

"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