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 exactly 8 correct answers of false?
a.
425
c.
500
b.
495
d.
515


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Answer:

Correct choice is b.

Step-by-step explanation:

Rafael is taking a test that contains a section of 12 true-false questions. Exactly 8 correct answers of false from 12 true-false questions have

$C_{8}^{12}=\dfrac{12!}{8!(12-8)!}=\dfrac{12!}{8!\cdot 4!}=\dfrac{8!\cdot 9\cdot 10\cdot 11\cdot 12}{8!\cdot 1\cdot 2\cdot 3\cdot 4}=9\cdot 5\cdot 11=495$

possible groups.