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This view is directly connected to all Valid quotes so it is important you keep your Quotes updated as you receive approvals and cancellations from your clients. Expand your Opportunity by hitting the + symbol to see Valid quotes under the selected option. You can uncheck Valid directly in this grid. Most likely is another field on a quote that you can check and uncheck when you have multiple options/quotes presented to a client. When you uncheck Valid it will auto uncheck Most Likely for you and remove from this report on the next refresh.
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In Summary, to remove an Opportunity from this grid you must use one of the methods below:
Cancel the project (completely dead)
Mark Quote as no longer Valid (part of the project was awarded but active quotes remaining are no longer active)
Push project through to be processed as an Order