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GATE Overflow Test Series | Mixed Subjects | Test 1 | Question: 29

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The topological order for the given hasse diagram is
$a\leq  \_\_ \leq \_\_ \leq d \leq  \_\_ \leq \_\_ \leq \_\_ \leq h.$

The first two blanks can be filled with $b$ and $c$ in any order, so $2!$ ways.

Next three blanks can be filled with $e,f$ and $g$ in any order, so $3!$ ways.

So, total orderings possible $= 2! * 3! = 12.$
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