The dry and brittle part is dead. Actually, that looks underwatered to me. The soil mix looks like it has a lot of peat in it. When peat dries out it can become hydrophobic and the cactus roots have trouble getting any water. A smaller pot with a grittier soil mix would be better for your plants. You can search this forum for advice on soil mixes. Plus, your cacti look like they need a bit more sun light than they are getting but if you increase the light then do it gradually. They can sunburn if they get too much sun too fast.

It's in bad soil and it has died. The other is looking quite unhappy at the base as well. My guess is its roots are in bad shape and dessicated from being underwatered. You'll need to repot it in some coarser, freely draining mix that can drain and dry out fast (a terra cotta pot helps with that as well). Once it's in a better pot and soil, water thoroughly, not just a few drops, and let it go dry again. It's too late for the dead one, but the other two can bounce back (the one on the right looks to be actively growing, so that's a good sign). Good luck!

Don't use that pot again. It's far too large. As Dannie said, get some small clay pots. I would pot them separately in the proper mix. (Commercial cactus/succulent mix combined 50/50 with perlite or pumice from your nursery.) The bad one has some new growth at the base? You might be able to repot that after cutting off the failing portion. Let it air dry a few days, then pot up and don't water until it has roots. Try it!

You have some nice plants there, and I hope you can save them.

Well, it´s dead. But some plants in the same container seem to be doing OK, which have obviously had the same conditions. We can only really guess at the reason, could even be some obscure infection, or no real reason at all, but like other folks say, your soil does look a bit suspect. There are as many favourite soil mixes as there are growers, and I have now firmly settled on a well-draining gritty mix with a good proportion of limestone for my desert cacti, with just a little organic material. I totally avoid soggy peat, which means any commercial ´cactus mix´, as they are invariably full of peat or even worse - ´forest product´- read sawdust. A gritty mix in unglazed terra cotta pots will set you up. Err on the dry side rather than overwater - it is quite difficult to kill a cactus through underwatering. They are succulents - they will store water when it rains heavily, then be well able to survive drought conditions for weeks or even months.