This is going to depend on the detailed facts of the situation. In particualr it will depend on what, if anything, is said in the sites terms and conditions, or terms of service (TOS) document. It will also depend on whether the mistaken price was so low that no reasonable person would have believed it to be a valid, intentional offer.
In the Lexology article "Oops! Pricing mistakes by online retailers" the authors say:
...what are the rules when a merchant accidentally advertises a lower price than intended? What right, if any, does the online retailer have to repudiate the apparent deal? After all, didn’t it make an offer to sell at a particular price that became a binding obligation when the buyer accepted the offer by tendering the purchase price?
In the first instance, there may or may not have been a binding offer and acceptance. Contracts 101 teaches that whether a communication from one party to another constitutes an actionable offer, as distinguished from mere preliminary communications or an invitation to make an offer, is a fact-intensive inquiry, looking at all the circumstances.
Some online retailers have adopted website terms and conditions that attempt to overcome such uncertainties by explicitly characterizing the customer’s order as the offer, thereby leaving the retailer free to reject it for any reason, including because the advertised price was erroneous. Others simply reserve the right to cancel orders, either for any reason or specifically where the posted price was erroneous. In addition, even absent such contractual hedges, under the common law doctrine of unilateral mistake of fact, a contract is voidable if its enforcement despite one party’s mistake regarding a material term such as price would be “unconscionable” or if the other party “had reason to know of the mistake . . . .” Thus, at least where a posted price is so egregiously low—or, in Razor’s case, a coupon so dramatically over-generous—that a reasonable consumer would suspect it is a mistake, this doctrine would entitle the retailer to repudiate the contract.
On the other hand, none of these safeguards is necessarily ironclad. The unilateral mistake doctrine is so obviously fact-dependent that in all but the most egregious circumstances, its applicability is likely to be disputable. Using agreed terms and conditions to avoid the otherwise-uncertain application of general contractual rules is a time-honored strategy. But online terms and conditions are both adhesive in nature and subject to special FTC rules requiring that they be “clear and conspicuous.” Thus, their enforceability is also inherently very fact-bound. And whatever protection the common law and artful drafting might provide in other circumstances, some states impose particular obligations on retailers when it comes to honoring the prices they advertise, however egregious the error.
In the Telegraph's story "Do retailers have to honour pricing mistakes?" it is said that:
The legally binding contract is complete when a retailer accepts an order. However, acceptance does not necessarily happen at the point of order. Even the confirmation email may not be an acceptance. Some retailers reserve the right to cancel an order up to the point of delivery. It is therefore important to carefully check the retailer’s terms and conditions (which must be available on their website) and emails – if a retailer simply acknowledges an order, there may be no contract at that point.
In short, this is a very fact-specific question, and the details of what was posted on the site of the firm involved will matter.