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In the grid shown, you move only right or up along the lines from A to B. The crossing marked X is closed. How many shortest routes avoid X?

Competition practicePermutations & Combinations

A126
B60
C66
D70

Step-by-Step Solution

All routes: 5 rights and 4 ups,

^{9} C_{4} = 126

. Routes through X at (2, 2):

^{4} C_{2} \times^{5} C_{2} = 6 \times 10 = 60

. Avoiding X:

126 - 60 = 66

.

Answer: C) 66

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