When Indefinite Numerals and Definite Numerals are used together, there order should be:
Indefinite Numerals (many, various, a lot of etc.) + Definite Numerals
Example: Many single rooms are booked for the team members. / No error
Explanation: According to the rule given above, there is no error in the sentence and the above sentence is correct.
The correct sentence is as follows:
Many single rooms are booked for the team members.