Can a person with a drivers permit in the state of Utah drive with other people in the car?

Yes but the seat next to you has to have the licensed 21 yr old:

Beginning on August 1, 2006, the division, upon receiving an application for a learner permit, may issue a learner permit effective for one year to an applicant who:

is at least 15 years of age;

has passed the knowledge test (written) required by the division;

has passed the medical and eye exam;

parent/legal guardian has signed for financial responsibility; and

has submitted a nonrefundable fee of $15.00 for a learner permit

The learner permit entitles an applicant that is younger than 18 years of age to operate a regular Class D motor vehicle only if:

an approved driving instructor is occuping the seat beside the applicant;

the applicant's parent or legal guardian, who must be a licensed driver, is occupying a seat beside the applicant; or

the responsible adult who has signed for financial responsibility, who must be a licensed driver; is occupying a seat beside the applicant;

allows for other passengers in the vehicle; and

the learner permit must be in the applicant's immediate possession

The learner permit entitles an applicant that is 18 years of age or older to operate a regular Class D motor vehicle only if:

a person 21 years of age or older, who must be a licensed driver, is occupying the seat beside the applicant; and

the learner permit must be in the applicant's immediate possession