Pascal triangle just got better

Probability Level 4

What will be the value of the $10^\text{th}$ expression (applying operation from left to right).

$\begin{array} {lc} \text{First expression} & 1 \\ \text{Second expression} &1\div1 \\ \text{Third expression} & 1\div2\div1 \\ \text{Fourth expression} & 1\div3\div3\div1\\ \text{Fifth expression} & 1\div4\div6\div4\div1\\ \text{Sixth expression} & 1\div5\div10\div10\div5\div1\\ \text{Seventh expression} & 1\div6\div15\div20\div15\div6\div1 \end{array}$

If you are getting answer like $w.xyz\times10^{a}$ after correction to three decimal places, then enter it as $w.xyzE+a$

Clarification: $E$ represents E notation

The answer is 8.504E-14.

1 solution

Alex G
Apr 26, 2016

The $(n+1)th$ row of Pascal's triangle is described as: $\large{ {n} \choose {0}}$ $\large{ {n}\choose {1}}$ ... $\large{ {n} \choose {n-1}}$ $\large{ {n} \choose {n}}$ .

Using this, we get: $\large{ {9} \choose {0}}$ $÷$ $\large{ {9} \choose {1}}$ $÷...÷$ $\large{ {9} \choose {9}}$ which can be evaluated to be $\frac {1} {11759522374656}$ or $8.503 E -14$

Pascal triangle just got better

The answer is 8.504E-14.

1 solution

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