Answer to Question #265373 in Algebra for Che

Question

A true-false quiz contains five questions. In how many ways can a student answer the questions if the student answers two of the questions with “false” and the other three with “true”

Answer 1

The number of questions in the quiz is 5.

The student answers two questions with "false" and the other three with "true".

If the student answers two questions with "false" it implies that he answered the other three with "true".

So, it is enough to find the number of ways of answering two question with "false".

Evaluate the number of ways of answering as follows.

Total no. of ways=no. of ways of answering two questions with false

$=5C_2\\\frac{5×4}{2×1}\\=10$

Therefore, the total number of ways of answering two questions with false and three questions with true is 10.