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7.
A set of four elements has 24 subsets, since for every element there are two options: it may, or may not, be in a subset. This set of subsets includes the empty set and the original set, and everything in between.
7 To make it a bit more intuitive, think of it like this: If you have a set of 7 elements, you can "turn it into" a set of 6 elements by removing one of the elements. So, in how many ways can you remove an element from the set of 7 elements, without making the same 6-element set more than once?
7
8 over 5, which is the same as 8 over 3 (where 3 is calculated as 8 - 5). In other words, (8 x 7 x 6) / (1 x 2 x 3).
7.
It has 27 = 128 subsets.
A set of four elements has 24 subsets, since for every element there are two options: it may, or may not, be in a subset. This set of subsets includes the empty set and the original set, and everything in between.
How many subsets are there in 2 3 5 7 11 13 17 19 23?
If your 7 element set is {a, b, c, d, e, f, g}, you would list a 3 element subset by taking any 3 elements of the set eg., {a, d, g} or {b, c, f}, etc. To count all of the subsets, the formula is 7C3, where 7C3 is 7!/(3!*4!), or 35 different unique 3 element subsets of a 7 element set.
118 elements.
7 To make it a bit more intuitive, think of it like this: If you have a set of 7 elements, you can "turn it into" a set of 6 elements by removing one of the elements. So, in how many ways can you remove an element from the set of 7 elements, without making the same 6-element set more than once?
Group 7 contains 5 elements, group 14 contains 6 elements, and group 18 contains 7 elements.
The number of subsets of a set is 2^number_elements_in_the_set. The set {1, 2, 3, 4, 5, 6, 7} has 7 elements, thus it has 2^7 = 128 possible subsets.
For a set with n members, there are 2n possible subsets; thus the set {1, 2, 3, 4, 5, 6, 7, 8, 9} has 9 members and 29 = 512 possible subsets.
7
There are 2^n elements, where n is the number of coins.