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If project team members increase from six to ten, by how many times is the number of communication paths increased?

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To understand the increase in communication paths when project team members increase from six to ten, it's essential to consider the formula for calculating the number of communication paths in a project team. The formula is given by:

\[ \text{Paths} = \frac{n(n-1)}{2} \]

where \( n \) is the number of team members.

Initially, with six team members:

\[ \text{Paths for 6 members} = \frac{6(6-1)}{2} = \frac{6 \times 5}{2} = 15 \]

Now, with ten team members:

\[ \text{Paths for 10 members} = \frac{10(10-1)}{2} = \frac{10 \times 9}{2} = 45 \]

To find the increase in communication paths, we subtract the initial number of paths from the latter:

\[ \text{Increase} = 45 - 15 = 30 \]

Now, to determine how many times the communication paths were increased, we consider the ratio of the new number of paths to the old number:

\[ \text{Ratio} = \frac{45}{15} = 3 \]

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