Question

Find the nos of four digit nos divisible by 4 obtained using 1,2,3,4,5 without repetation?

Answer 1

80

Explanation:

A number is divisible by 4 if the last 2 digits of it are divisible by 4. For instance, 524 is divisible by 4 `(524-:4=131)`

With the numbers listed, we can make the following 2-digit numbers that are divisible by 4:

12, 24, 32, 52

And so there are 4 ways to make numbers divisible by 4. So that's the final 2-digits of the numbers we're making.

Now to the first 2 digits. For each ending number (like the 12), we have 3 numbers remaining and we're going to pick 2. Order matters (5412 is different from 4512) and so it's a permutation:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

and so

`P_(5,2)=(5!)/(3!)=20` ways to order the first 2 digits for each of the remaining 2 digit sets.

This gives

`20xx4=80` ways to make a 4-digit number that is divisible by 4.