(a) \(10!/(2!4!)=75600\).

(b) The EEEE block cannot lie between the Rs, which enclose exactly three letters. Choose and order three of the four distinct single letters G,N,A,T between the Rs in \(4P_3=4!=24\) ways. Arrange the R...R block, EEEE block and remaining single letter in \(3!\) ways: \(24(6)=144\).

(c) There are two alternating patterns, each with \(5!/2!\) consonant arrangements and \(5!/4!\) vowel arrangements. \[P=\frac{2(5!/2!)(5!/4!)}{75600}=\frac{600}{75600}=\frac1{126}=0.00794.\]