(a) The word CROCODILE consists of 9 letters where C and O are repeated. The formula for permutations of a multiset is given by:

\(\frac{9!}{2!2!}\)

Calculating this gives:

\(\frac{362880}{4} = 90,720\)

(b) To find the number of arrangements with C at each end and the two Os not together, we use the following method:

First, fix C at both ends, leaving 7 positions to fill with the letters R, O, C, O, D, I, L.

Calculate the total arrangements of these 7 letters:

\(\frac{7!}{2!} = 2520\)

Now, calculate the arrangements where the two Os are together. Treat the two Os as a single unit, so we have 6 units to arrange: (OO), R, C, D, I, L.

Calculate the arrangements of these 6 units:

\(6! = 720\)

Subtract the arrangements where Os are together from the total arrangements:

\(2520 - 720 = 1800\)