Yes, with a caveat. The 50A wire and plug is more than heavy enough for the dryer, so there is no problem there.
The possible problem is that the dryer is designed to be protected by a 30A breaker. In the event of failure in the dryer, the breaker may not trip as it is oversized. The best solution? Get a small breaker box from a home center and mount a 30A breaker in it. Mount it on the back of the dryer, run the 50A cord into the feed lugs of the box, and connect the dryer feed to the 30A breaker. This way you can plug the dryer into the 50A outlet like you want, and the dryer is protected with a 30A breaker as usual. You can get small breaker boxes or fused disconnects without too much cost. Just make sure the breaker box / disconnect panel is rated to 50A, as you want to feed it off a 50A circuit.
As long as the voltage requirement of the dryer matches the voltage of the outlet (which is presumably 240 volts), then yes. The amp rating of the cord and outlet is merely the maximun current (amps) allowed. You're well under that with 24 amps.
For convenience I install the receptacle just above the backboard of the dryer. This way if the dryer is to be moved out of its location it can be unplugged before the move is started. Sometimes the dryer is located in a confined space and it is hard to reach down to the floor level to unplug the dryer with out becoming an acrobat.
There is a couple of things going on here. First a 30 amp dryer plug will not fit into a 50 amp range plug. So rather than changing the the dryer cord over to a 50 amp range cord all you have to do is change the 50 amp breaker over to a 30 amp breaker in the distribution panel. The wire size is big enough to run the 30 amp dryer. Change the 50 amp range receptacle to a new 30 amp dryer receptacle and your installation will be within the electrical code guidelines.Circuit breakers and wire gauges are designed to protect the wiring, not the appliance (and not the user!). Amperage ratings are draws, not demands.More InformationThe answer to your question is yes. A 30-amp dryer will run quite nicely on a 50-amp circuit, provided it is properly wired and the voltage is correct. As has been pointed out, a standard 30-amp dryer pigtail won't plug into a standard 50-amp range receptacle. But there is no reason you can't replace the dryer's pigtail with a range pigtail, and that would be a heck of a lot easier and faster -- and cheaper! -- than replacing receptacle and breaker, as suggested above.What you must NEVER do is the opposite -- replace a range pigtail with a dryer pigtail and try to run the range on a 30-amp circuit. Most electric ranges can draw up to 50 amps, enough to overload the 30-amp circuitry usually provided for a clothes dryer.The key here is understanding how current draw works. A 50-amp appliance plugged into a 30-amp circuit -- say, an electric stove plugged into an outlet meant for a dryer -- can be a problem because the the stove will try to draw more current through the circuit than it's rated for, and protected against. A circuit breaker will trip, or a wire or connection will overheat.On the other hand, a 30-amp appliance plugged into a 50-amp circuit -- a clothes dryer plugged into a stove outlet, for example -- is just fine. The dryer will draw a mere 30 amps, no matter that the circuit can provide 50 amps.
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