Is it permissible to sell services such as design, writing, and programming, the details of which are not known except upon the client's request, and then contract with a third party to complete them for a lower price, knowing that payment is not made until after the service is delivered and the client approves it?

It is permissible for a person to agree to perform a specific task, then entrust it to someone else to do for a lower wage, because it is an act of hiring for work to be done (in a person's responsibility). An example of this is cleaning a house, unless the intention was for the first worker to perform the work himself, or if his selection was intended due to a special quality the hirer sought in him, such as hiring a well-known calligrapher. This is supported by the statement of Sheikh Ibn Uthaymeen in "Al-Sharh Al-Mumti'": "If a person is hired for work to be done (in his responsibility)... it is permissible." He also differentiated between a person selling goods he does not own and contracting for work to be done, such as in hiring (Ijarah (definition)) and manufacturing contracts (Istisna').