Outlook Live accounts have historically been 500 recipients per day. Microsoft has recently updated this policy to be in line with the Exchange Online offering in Office 365. All newly provisioned tenants will see these new limits immediately. For those customers who are already on Live@EDU, you should either see these now or you will see the changes over the upcoming weeks.
For some additional information about limits and options for supporting bulk email please refer to articles shown below.
There is a recipient rate limit, often called a sender limit or sending limit, for cloud-based e-mail accounts. This limit defines the maximum number of recipients that can receive e-mail messages sent from a single cloud-based account in a 24-hour period. The recipient rate limit for Exchange Online is 1,500 recipients per day.