(later edit of my answer: for a newer photographer, most of the suggestions made in this thread including mine are overkill. For a trip like this, something like a T5i (or choose a body. APS sensor is fine), the 24-105, and the Canon 100-400 would be a great setup and cover pretty much any need you could have that wouldn't require $10,000 lenses to shoot. And that set would cost about the same as just a 70-200 F2.8L IS II, which is why my suggestion on retrospect wasn't a good one. If you're a more advanced photographer? Maybe. But for a new one? the 100-400 is a great option and will solve the problems he asked about and the ones we're trying to solve for him...)

You're going to be in situations where tripods are going to be unrealistic. That generally means you should lean towards an IS lens over a faster non-IS lens.

Something not covered by others here: you're going to Africa. You have to carry all this gear. For an experienced photographer, renting a 500mm and hauling it to Africa is do-able. for a new person who's never done this before? That can be a challenge. Remember, you don't want to pack it, it has to carry on (with all your other photo and electronics gear you don't want to disappear), and that turns into a hassle fast.

My thought: buy the 24-105 lens. It's a good all around lens. The 70-200F4 is a good second lens that goes well with it. You can put a 1.4x teleconverter on it to push it to 320 F5.6 and it'll work okay.

But what I'd consider doing for this trip: RENT the 70-200 F2.8L IS II and a 2.0X teleconverter and use those instead of the 70-200 F4. the 70-200 F2.8Lis a lot bigger and heavier than the F4, but it's faster, and the IS II version handles a 2.0x tele fine, so you get that extra reach with a 400 F5.6 equivalent, and it's a really sharp combo. (note: IS II, not the older IS. the older IS isn't sharp enough to use like this).

Even better, you do that without adding a big, heavy third lens to your setup, saving you a hunk of weight and hassle. My pack (7D, T3i, 24-105, 70-200F2.8L IS II, 20.x) lives in a backpack with all of the other stuff you need to carry and weighs in at just under 20 pounds. If you add a 400mm or 500mm prime, you'll need a bigger pack that might not fit carryon capabilities (or a second person to also carry camera gear in a second pack), and you're now well over 25 pounds of gear headed towards 30 pounds.

So don't just think about what lenses, think about where this person is going and what they need to do to get there. Which makes it even more complicated. you certainly odn't want to BUY the big, heavy 70-200, but this is a perfect opportunity to rent one and solve the weight/bulk problem while still getting a reasonably big hunk of glass that goes to 400mm.

(and then I'd probably but the 70-200F4 as my every day lens when I got back... It's great, unless you need to push it to 400mm with a teleconverter...)