a) How many ways are there of tiling a 2x10 rectangle 1x2 tiles of which 4 are e

ID: 3282944 • Letter: A

Question

a) How many ways are there of tiling a 2x10 rectangle 1x2 tiles of which 4 are exactly vertical?

b) How many ways are there of tiling a 2x13 rectangle 1x2 tiles?

c) How many ways are there of tiling a 3x13 rectangle 1x3 tiles?

d) How many ways are there of tiling a 3x14 rectangle 1x2 tiles?

e) Which of the following (0; 100; 10000; 1000000; or 100000000) is closest to the number of ways of tiling a 5x14 rectangle with 1x4 tiles? Why?

f) How many ways are there of building a 2x2x14 solid from 1x1x2 blocks?

A) Here considering a Tile of 2*10 now we have the condition four tiles is always vertical .

To fill the the rectangle of 2*10 we need 10 1*2 tiles (vertically)using concept of p &c we can have 10C4

which comes out to be 210.

B, C,D can be done with the similar approach .

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