$^{6} C_{3} +^{6} C_{2} =$ $- -------- -$

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Solution

$^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1^{m} C_{1} & ^{m + 3} C_{1} & ^{m + 6} C_{1}^{m} C_{2} & ^{m + 3} C_{2} & ^{m + 6} C_{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 2^{α} 3^{β} 5^{γ}

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1^{m} C_{1} & ^{m + 3} C_{1} & ^{m + 6} C_{1}^{m} C_{2} & ^{m + 3} C_{2} & ^{m + 6} C_{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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