Where does Bittrex/Binance (alternative cryptocurrency markets) get their coins? There are several cryptocurrency platforms like Bittrex, Binance where you can transfer your BTCs (or other mainstream coin types such as ETH, LTC) to and buy alternative coins (IOTA, XRP or thousand other types) in exchange. Where do these platforms get their alternative coins?

Are they just selling coins that they had bought from people (similar to coinbase's approach see [1]) who got them through ICOs or several other channels? What would those channels be?
Pure exchange like Bittrex neither need, or have use for a huge reserves of cryptocurrencies. Their service model is based on providing a platform for peers to sell and buy coins/tokens.
Also, they don't actually buy the coins from the sellers. Sellers/buyers are the one's who deposit coins to Bittrex's wallet, so Bittrex act like an intermediary between the seller and buyer.
There is an exception though, you can actually wire transfer to Bittrex and buy USDT, and they will purchase on your behalf from other sellers on a per-order basis.

Coinbase is different, they are more like a bank-hybrid with their own dedicated exchange(GDAX), and as a bank , they have a huge reserves of cryptocurrencies as they deal with buyers/sellers directly.