Answer: 374416
Step-by-step explanation:
Given : A test requires that you answer first Part A and then either Part B or Part C.
Part A consists of 4 true false questions, Part B consists of 6 multiple-choice questions with one correct answer out of five, and Part C consists of 5 multiple-choice questions with one correct answer out of six.
i.e. 2 ways to answer each question in Part A.
For 4 questions, Number of ways to answer Part A = [tex]2^4[/tex]
5 ways to answer each question in Part B.
For 6 questions, Number of ways to answer Part B = [tex]5^6[/tex]
6 ways to answer each question in Part C.
For 5 questions, Number of ways to answer Part C = [tex]6^5[/tex]
Now, the number of ways to completed answer sheets are possible :_
[tex]2^4\times5^6+2^4\times6^5\\\\=2^4(5^6+6^5)\\\\=16(15625+7776)\\\\=16(23401)=374416[/tex]
Hence, the number of ways to completed answer sheets are possible = 374416
