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If you stick to the Mountain track which starts from near the visitor centre you should be fine. There aren't any steep drops(didn't see one when I last climbed in August 2011) per se but there are drops nonetheless. But most of the drops are before the halfway mark. After the halfway mark it is more or less like a zig zag way winding up the mountain.
Here's a fly through of the tourist route on youtube. If you watch the brief video or any of the other real life videos of the hike, it should reassure your friends that there is nothing to fear.
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