it ntirely depends on the nature of the persons problems. they really look at both care and mobility seperately, and if it's not usually awarded seperately it will be because the people applying have problems with both care AND mobility which can often go hand in hand.
Afriend of mine who i know through the arthritis group has the care component because mainly her arms are affected, meaning she cannot lift pans, turn taps on, wash her hair. However, hr legs are ok, so she wouldnt expect to get any mobility component - she can walk just fine