Question

Rafael is taking a test that contains a section of 12 true-false questions. How many of the possible groups of answers to these questions have at least 6 correct answers of true?

a.
2510
b.
2545
c.
2450
d.
2300


Please select the best answer from the choices provided

A
B
C
D

Answer 1

A

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

`C_6^(12)=(12!)/(6!(12-6)!)=924,\\ \\C_7^(12)=(12!)/(7!(12-7)!)=792,\\ \\C_8^(12)=(12!)/(8!(12-8)!)=495,\\ \\C_9^(12)=(12!)/(9!(12-9)!)=220,\\ \\C_(10)^(12)=(12!)/(10!(12-10)!)=66,\\ \\C_(11)^(12)=(12!)/(11!(12-11)!)=12,\\ \\C_(12)^(12)=(12!)/(12!(12-12)!)=1.`

Hence there are

`924+792+495+220+66+12+1=2510`

possible groups.