Minus One Makes A Difference

Discrete Mathematics Level 2

\[\left( \frac { 71 }{ 1 } -1 \right) \left( \frac { 71 }{ 2 } -1 \right) \left( \frac { 71 }{ 3 } -1 \right) \cdots \left( \frac { 71 }{ 42 } -1 \right) \left( \frac { 71 }{ 43 } -1 \right) \]

Which of the following is equal to the above value?

Notation: \( \binom MN \) denotes the binomial coefficient, \( \binom MN = \frac{M!}{N!(M-N)!} \).

\[\left( \begin{matrix} 71 \\ 43 \end{matrix} \right) \] \[\frac { 44 }{ 71 } \left( \begin{matrix} 71 \\ 44 \end{matrix} \right) \] \[ \frac { 44 }{ 71 } \left( \begin{matrix} 71 \\ 43 \end{matrix} \right) \] \[\frac { { 71 }^{ 43 } }{ 43! } \] \[\left( \begin{matrix} 71 \\ 44 \end{matrix} \right) \]

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