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How many subsets are in the set 12345?
Number of subsets with no members = 1Number of subsets with one member = 5.Number of subsets with 2 members = (5 x 4)/2 = 10.Number of subsets with 3 members = (5 x 4 x 3 /(3 x 2) = 10.Number of subsets with 4 members = (5 x 4 x 3 x 2)/(4 x 3 x 2) = 5.Number of subsets with 5 members = 1Total subsets = 1 + 5 + 10 + 10 + 5 + 1= 32.A set with n elements has 2n subsets. In this case n = 5 and 25 = 32.The proof in the case that n = 5 uses a basic counting technique which say that if you have five things to do, multiply together the number of ways to do each step to get the total number of ways all 5 steps can be completed.In this case you want to make a subset of {1,2,3,4,5} and the five steps consist of deciding for each of the 5 numbers whether or not to put it in the subset. At each step you have two choices: put it in or leave it out.
How many subsets containing an odd number of elements does a set with 10 elements have?
Well, honey, a set with 10 elements will have 2^10 or 1024 subsets in total. Now, if we want to count just the subsets with an odd number of elements, we need to consider that for each element, you have the option of including it or not. So, you're looking at 2^9 or 512 subsets with an odd number of elements. Hope that clears things up for ya, darling.
How many different 10 element subsets can be made from a set of 15 sets?
That is the same as asking 15C10 which is 3003. It is 15! divided by (15-10)!(10!) This is 15x14x13x12x11 divided by 5x4x3x2x1 or divided by 120 or 360360=3003
Rectangle A is width 4 and length 8 so draw similar rectangle scale factor 2.5?
Draw a 10 x 20 rectangle.
How many subsets of set A that contain exacly 3 elements set A has 10 elements?
You have three choices at a time without repeats. To do this multiply 10x9x8=720. This will give you duplicates, so divide the result by 1x2x3.
