PowerShell Where-Object $_.name -like -in $list - powershell

Question

I am new to PowerShell and ran into a bit of a roadblock. I am trying to pull program name and version information from multiple servers.
I have a list of the program names in a $list variable, but the program names also contain the version numbers in them. I am just storing the names of the programs in the list variable without the version numbers.
I am trying to figure out a way to use both the -like and -in parameters with the Where-Object cmdlet in order to match the full program entry name (e.g. AdToUserCacheSync 1.10.1.10) with my entry in the $list variable (e.g. AdToUserCacheSync).
How can I do this?
$list = Get-Content "\\server\c$\temp\list.txt"
$storeTestServers = Get-Content "\\server\c$\temp\testStores.txt"
foreach ($server in $storeTestServers) {
Get-WmiObject -Class Win32_Product -ComputerName $server |
Select-Object -Property PSComputerName, Name, Version |
Where-Object {$_.pscomputername -like "940*" -and $_.name -like -in "*$list*"}
}

Answer 1

The Where-Object FilterScript block is just a scriptblock that returns $true, $false or nothing - you can do all kinds of crazy things inside it, including looping over an array to see if there is a wildcard match in one of the entries:
Where-Object {
$ProductName = $_.Name
$_.pscomputername -like "940*" -and (
$list | ForEach-Object {
if($ProductName -like "*$_*"){ return $true }
}
)
}

Answer 2

I found the Adobe version by PowerShell:
Get-WmiObject -Class Win32_Product -ComputerName 127.0.0.1 |
Select-Object -Property PSComputerName, Name, Version |
Where-Object {$_.Name -like "Adobe*"} | Out-File Adobe_Log.log