Charging rent for whole month or half

[Lue Brooks]

I am finally getting closer to finally renting out my duplex. After finally selecting an applicant Who was supposed to move in Nov, 1,2018 they have said they haven't put in their 30 day notice yet so can not move in until Nov 20th. They have not put down their security deposit yet. The deposit is half of the rent. My question is can I take the deposit and let them sign the lease and still collect the whole rent? or am I only allowed to take the deposit and charge for the amount of days they actually move in and start living there?