Question

AN ENGLISH EXAM CONSISTS OF TEN ESSAY QYESTIONS. IF A STUDENT MUST CHOOSE 4 OF THE 10 QUESTIONS HOW MANY DIFFERENT SETS OF 4 QUESTIONS ARE AVAILABLE?

Answer 1

Given

Number of questions in an english exam = 10

Find

Number of different sets of 4 questions are available.

Step-by-step explanation

as we have given that a student must choose 4 of the 10 questions.

so , number of different set of 4 questions are available =

`^(10)C_4`

so ,

`\begin{gathered} ^(10)C_4=(10!)/(4!(10-4)!) \\ \\ ^(10)C_4=(10!)/(4!6!) \\ \\ ^(10)C_4=(10*9*8*7*6!)/(4*3*2*1*6!) \\ \\ ^(10)C_4=(5040)/(24) \\ \\ ^(10)C_4=210 \end{gathered}`

Final Answer

Hence , the number of different sets of 4 questions are available are 210