Final answer:
The clause among the given groups of words is 'we signed up' because it includes a subject and a verb, which are the necessary components of a clause.
Step-by-step explanation:
The group of words that constitutes a clause is 'we signed up' because it contains both a subject ('we') and a verb ('signed up'). A clause is defined as any group of words that includes a subject and a verb, which can be either independent or dependent. 'Arriving at the office' and 'for three jobs' do not form clauses by themselves as they lack either a subject or a verb, making them phrases rather than clauses. Therefore, these groups of words don't meet the criteria of a clause which needs to have both components to qualify.