Question

A student is told to work any 6 out of 10questions on an exam. In how manydifferent ways can he complete the exam?The correctness of his answers has nobearing.)A) 1,000,000B) 24D) 5040C) 210

Answer 1

Given:

Number of questions = 10

Number of ways = 6

Let's find the different number of ways he can complete the exam.

To find the number of aysm, we are to use the combination formula:

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

Where:

n = 10

r = 6

Hence, we have:

`\begin{gathered} ^(10)C_6=(10!)/(6!(10-6)!) \\ \\ =(10!)/(6!(4)!) \\ \\ =(10*9*8*7*6!)/(6!(4*3*2*1)) \\ \\ =(10*9*8*7)/(4*3*2*1) \\ \\ =(5040)/(24) \\ \\ =210 \end{gathered}`

Therefore, the number of ways he can complete the exam is 210 ways.

ANSWER:

210