Answer:
A
Step-by-step explanation:
Rafael is taking a test that contains a section of 12 true-false questions. At least 6 correct answers of true means that 6 answers are true, 7 are true, 8 are true, 9 are true, 10 are true, 11 are true or 12 are true.
Then
[tex]C_6^{12}=\dfrac{12!}{6!(12-6)!}=924,\\ \\C_7^{12}=\dfrac{12!}{7!(12-7)!}=792,\\ \\C_8^{12}=\dfrac{12!}{8!(12-8)!}=495,\\ \\C_9^{12}=\dfrac{12!}{9!(12-9)!}=220,\\ \\C_{10}^{12}=\dfrac{12!}{10!(12-10)!}=66,\\ \\C_{11}^{12}=\dfrac{12!}{11!(12-11)!}=12,\\ \\C_{12}^{12}=\dfrac{12!}{12!(12-12)!}=1.[/tex]
Hence there are
[tex]924+792+495+220+66+12+1=2510[/tex]
possible groups.
