Asking for Permissions

Let's get a permission.

すみません / Sumimasen
Excuse me.

〜　(し)　て　いい　ですか?/ ~te ii desu ka?
Can I ~?

すみません。しゃしん　(を)　とって　いい　ですか？/ Sumimasen. Shashin (wo) totte ii desu ka?
Can I take a picture?

すみません。ここ　(に)　すわって　いい　ですか？/ Sumimasen. Koko (ni) suwatte ii desu ka?
Can I sit here?

"wo" and "ni" are frequently omitted in conversation but they show the action's purpose and indicating place, object, or reason.