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Question

In a game, a person P at point (x,y) can jump to any one of the following points respectively: (x+1,y),(x+2,y),(x,y+1),(x,y+2). If P is at (0,0), then he can reach:


A
(2,2) in 14 ways
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B
(2,3) in 32 ways
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C
(2,2) in 9 ways
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D
(2,3) in 26 ways
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Solution

The correct options are
A (2,2) in 14 ways
B (2,3) in 32 ways
Let's denote the respective jumps as L1,L2,U1,U2.

For (2,2):
L1L1U1U14!2!2!L1L1U23!2!L2U1U13!2!L2U22!

Total =6+3+3+2=14 ways

For (2,3):
L1L1U1U1U15!3!2!L1L1U1U24!2!L2U1U1U14!3!L2U1U23!

Total =10+12+4+6=32 ways

Mathematics

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