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:

$\begin{gathered} =^nC_r \\ \\ =\frac{n!}{r!(n-r)!} \end{gathered}$

The value is,

$\begin{gathered} =^{10}C_6 \\ \\ =\frac{10!}{6!(10-6)!} \\ \\ =\frac{10\times9\times8\times7\times6!}{6!\times4!} \\ \\ =\frac{10\times9\times8\times7}{4\times3\times2} \\ \\ =210 \end{gathered}$

So the value is 210.