Easy as ABC

Probability Level pending

You have three colors and three letters.

How many ways can you color, and place letters in, a 3x3 grid such that the following hold?

  • No row or column has the same letter
  • No row or column has the same color
  • No two boxes have the same color and letter (i.e. If one red box contains a C, you can't have another red box containing a C)

Above is one way to do this.

How many ways are there to do this all together?


The answer is 72.

Geoff Pilling by Geoff Pilling , 53, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Geoff Pilling
May 12, 2017

There are six ways to choose the first row, and two ways to choose any one of the remaining six squares. After that, there is only one choice for the remaining colors.

So, that is 6 ⋅ 2 = 12 6 \cdot 2 = 12 ways so far.

Finally, for a given color, there are six ways to label them with A, B, and C.

Then there is only one way to put in the remaining letters.

So, there are 6 ⋅ 2 ⋅ 6 = 72 6 \cdot 2 \cdot 6 = \boxed{72} ways.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...