Two kind of tiles 1 x 1 and 2 x 2 we use them to cover the

Two kind of tiles : 1 x 1 and 2 x 2, we use them to cover the 8 x 3 without overlapping

How many different ways to arrange tiles here ?

Solution

Ways:

1) using all 1x1 tiles - one way

2)using one 2x2 tile and remaining 1x1 tiles = 2*7 = 14 ways

3) using two 2x2 tile and remaining 1x1 tiles = 16 ways

4) using three 2x2 tile and remaining 1x1 tiles =12 ways

5)using four 2x2 tile and remaining 1x1 tiles =10ways

Thats all the possible cases

so total ways = 1+16+14+12+10 =53