Question

A student is told to work any 6 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.)A) 1,000,000B) 24D) 5040C) 210

Answer 1

Given:

Total question = 10

Work on question = 6

Find-:

How man different ways can complete the exam

Explanation-:

A number of ways of choosing 6 forms 10 is:

`=^(10)C_6`

So, the value is:

`\begin{gathered} =^nC_r \\ \\ =(n!)/(r!(n-r)!) \end{gathered}`

The value is,

`\begin{gathered} =^(10)C_6 \\ \\ =(10!)/(6!(10-6)!) \\ \\ =(10*9*8*7*6!)/(6!*4!) \\ \\ =(10*9*8*7)/(4*3*2) \\ \\ =210 \end{gathered}`

So the value is 210.