Carnations last far longer than daisies after being cut and put into a vase. Carnations can last up to four weeks, although most last only seven to 14 days. Daisies generally last only five to seven days. You can keep both daisies and carnations in a vase, but the daisies will probably die before the carnations even if you take excellent care of both flowers.
If you want to prolong the lives of the flowers, change the water in your vase regularly. Both carnations and daisies live longer if you give them fresh water daily. Daisies need a lot of water -- make sure to fill the vase. Remove dead leaves and petals from the water when you change it so that bacteria doesn't grow in the vase and kill the flowers faster.
Another trick for prolonging the life of your flowers is to cut the stems daily. Cutting stems helps the flowers absorb water more easily. Cut about 3/4 inch off daisy stems on a daily basis to help them absorb water. Cut carnations under running water and cut them above one of the nodes on the carnation's stalk.
Carnations are very sensitive to ethylene, a gas fruits and vegetables produce that is harmless to humans. Thus, if you want them to live a long time, keep the flowers away from other produce in your home. Cleaning the water in the flower base also helps reduce ethylene emissions, as dead leaves also emit this gas. Daisies do not have the same sensitivity to ethylene that carnations have.