Answer
a) 729
b) 256
c) 1024
d) 64
Work Step by Step
RNA sequence is a sequence of letters, each of which is one of A, C, G, or U. Thus by the product rule there are $4^6$ RNA possible sequences of length six.
a) If U is excluded, then each position can be chosen from among three letters, rather than four. Therefore the answer is $3^6$ = 729.
b) If the last two letters are specified, then we get to choose only four letters, rather than six, so the answer is $4^4$ = 256.
c) If the first letter is specified, then we get to choose only five letters, rather than six, so the answer is $4^5$ = 1024.
d)If only A or U is allowed in each position, then there are just two choices at each of six stages, so the answer is $2^6$ = 64.
