The set S has 5 elements. In how many ways can one select two (possibly identical) subsets of S whose union is S? 32 63 64 93 122

shashank.ism wrote:The set S has 5 elements. In how many ways can one select two (possibly identical) subsets of S whose union is S? 32 63 64 93 122 Let the elements be a,b,c,d,e. Now, (i am guessing)possibly identical means 3 in one set and 2 in another.[since union has to be S] This can be done in 5C3 ways = 10 ways.(none of the answer choice) Shashank,can you clarify this statement:-select two (possibly identical) subsets of S whose union is S? What dopes possibly identical mean?

harsh.champ wrote:shashank.ism wrote:The set S has 5 elements. In how many ways can one select two (possibly identical) subsets of S whose union is S? 32 63 64 93 122 Let the elements be a,b,c,d,e. Now, (i am guessing)possibly identical means 3 in one set and 2 in another.[since union has to be S] This can be done in 5C3 ways = 10 ways.(none of the answer choice) Shashank,can you clarify this statement:-select two (possibly identical) subsets of S whose union is S? What dopes possibly identical mean? I'm assuming that by "possibly identical" the problem means that the order of the sets is relevant (ie S1 = a,b and S2=c,d,e should be counted as well as S1=c,d,e and S2=a,b) Looking at it from the perspective of subset S1 after we choose the values in set S1, set S2 is determined. Thus it is just how many different ways can you select sets of size 0,1,2,3,4 or 5 from a group of 5 objects. 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 1 + 5 + 10 + 10 + 5 + 1 =32