**Question:**

There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect answers are there to this question?

**Solution:**

To find: number of possibilities of a selection of answers

Each item in column $\mathrm{A}$ can select another item in column $\mathrm{B}$.

Therefore the question involves selecting each item from column $\mathrm{A}$ to each item in column $B$. this can be done in $P(6,6)$

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, a permutation of 6 different objects in 6 places is

$P(6,6)=\frac{6 !}{(6-6) !}$

$=\frac{6 !}{0 !}=\frac{720}{1}=720$

Therefore, the possible number of selecting an incorrect or correct answer is 720.