Question

An essay test has 10 questions. Students are required to answer 7 out of the 10 questions. How many different sets of questions could be answered ?

Answer 1

Given:

The total number of questions is 10.

Students are required to answer 7 out of the 10 questions.

To find: The number of different sets of questions.

Step-by-step explanation:

We can use the combination formula,

`^nC_r=(n!)/((n-r)!r!)`

Substitute n = 10 and r = 7 we get

`\begin{gathered} ^(10)C_7=(10!)/((10-7)!7!) \\ =(10!)/(3!7!) \\ =(8*9*10)/(1*2*3) \\ =4*3*10 \\ =120 \end{gathered}`

Thus, the number of different sets of questions is 120.

Final answer: 120 sets