Question: Can I receive help with these problems? A multiple-choice quiz has 10 questions with four possible answer choices for each question. a. How many different

Can I receive help with these problems?

A multiple-choice quiz has 10 questions with four possible answer choices for each question. a. How many different ways can the quiz be completed if one answer choice must be selected for each question? b. How many different ways can the quiz be completed if up to one answer choice is selected for each question? (So, a question could be left blank.) How many positive integers not exceeding 1000 are divisible by either 4 or 6? (Hint: use the principle of inclusion-exclusion.) The protein-coded strand of an average human gene consists of 1,350 nucleotides. If each nucleotide can be any one of four different proteins (adanine, thymine, guanine, and cytosine], how many different genes with exactly 1,350 nucleotides are possible? (That is, how many 1,350-character sequences are there where each character can be A, T, G, or C?)

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