If set A={2,2,2,....,n times} , set B={4,4,4,4....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
Options:  A) a) k(n+m+mn)+ k  B) b) k^2(mn+n/m)  C) c) (1+n+m+mn)(k+1)  D) d) kmn(k+m+n)  E) e) None of the above.
a) how many 2's are included?   b) how many 3's are included?   and   c) how many 11's are included?   For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.   NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.   The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:   (mn + m + n + 1)(k + 1).   Mike   c) (1+n+m+mn)(k+1)
<result>C</result>
If set A={2,2,2,....,n times} , set B={4,4,4,4....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?