while converting 'n' state NFA into DFA you can get almost 2n states only. and those states are final states in DFA which contain atleast one final state of DFA. therefore this problem turned into no.of subsets of {a,b,c,d,e} which contain either d or e
= 24(for d) + 24 ( for e ) - 23 ( which are common for both d and e)
= 16+16-8
= 24