Quant Question of the Day Chat

Here you go!

The solution to this question involves two steps -

Step 01: Create four groups of two people in each group
Step 02: Divide four tasks among the four groups

1) Create four groups of two people in each group

We can do this in

8! / [(2)^4 * 4!]

If you’re wondering how did I arrive at this value, follow along, or else skip to step 2.

Let’s assume we have four boxes and 8 distinct balls. We have to put two balls in each box.

_ _ _ _

The first box can be filled in 8C2 ways
The second box can be filled in 6C2 ways (We have already selected 2 balls from the available 8, hence for the second box can be filled with two out of six remaining balls)
The third box can be filled in 4C2 ways
The fourth box can be filled in 2C2 ways

Now as we have considered a specific arrangement, divide by 4! to de-arrange the positions.

So, total way of forming the groups =

8C2 * 6C2 * 4C2 * 2C2 * (1/4!) = 8! / [(2)^4 * 4!]

2) Once you’ve created four groups of two people each, we can divide four tasks among the group the task in 4! ways.

So the total number of ways of performing both steps =

8! / [(2)^4 * 4!] * 4! = 8! / 2^4 = 2520

Option E.