There are 6 items in column A and 6 items in column B. A student is as

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?

Answer»

Given : The number of items in column A = 6 and in column B = 6

A student is asked to match each item in column A with an item in column B

To find : Possible number of correct or incorrect answers which he can give

Let the items of column A are fixed i.e. they arrangement is not changing

Now,

We just have to arrange items of column B

Formula used :

Number of arrangements of n things taken all at a time = P(n, n)

P(n,r) = \(\frac{n!}{(n-r)!}\)

∴ The total number of ways in which this can be done

= the number of arrangements of 6 things taken all at a time

= P(6, 6)

= \(\frac{6!}{(6-6)!}\)

= \(\frac{6!}{0!}\)

{∵ 0! = 1}

= 6 × 5 × 4 × 3 × 2 × 1

= 720

Hence,

Possible number of correct or incorrect answers which a student can give are 720.