Competition problem — Combinatorics

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Combinatorics Difficulty 3.9 AMC 10/12 Find the answer United States

Problem:
Suppose $a, b, c, d$ , and $e$ are objects that we can multiply together, but the multiplication doesn't necessarily satisfy the associative law, i.e. $(x y) z$ does not necessarily equal $x(y z)$ . How many different ways are there to interpret the product $a b c d e$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
$C$ (number of letters $-1$ ) $= C(4) = 14$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.