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In the grid shown, how many shortest routes from A to B pass through the point C?

Competition practicePermutations & Combinations

A56
B13
C60
D30

Step-by-Step Solution

A→

C

: 2 right, 1 up →

^{3} C_{1} = 3. C

→B: 3 right, 2 up →

^{5} C_{2} = 10

. Through

C : 3 \times 10 = 30

. (56 counts all routes A→B.)

Answer: D) 30

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