Consider the 2-out-of-5 error detection code. In this code, each codeword is 5-bit long; 2 out of 5 bits are 1s and the others are 0s. For example, 11000 is a valid codeword, but 01110 is not.

a. List all the valid codewords.

b. What fraction of errors is undetectable by this code, i.e., what is the FUE of this code? Justify your answer.

c. What fraction of 4-bit errors is undetectable by this code, i.e., what is the FUE(M=4) of this code? Justify your answer.