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The subsets of the set {s, t, u} consisting of the three elements s, t
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29 Sep 2021, 04:16
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The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?
The subsets of the set {s, t, u} consisting of the three elements s, t
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29 Sep 2021, 05:13
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Carcass wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?
A. 4 B. 7 C. 8 D. 15 E. 16
Take the task of building subsets and break it into stages.
Stage 1: Determine whether or not to place "t" in the subset The question tells us that "t" cannot be in the subset. So, we can complete stage 1 in 1 way (that is, we DO NOT place "t" in the subset
Stage 2: Determine whether or not to place "s" in the subset We can either HAVE "s" in the subset or NOT HAVE "s" in the subset So, we can complete stage 2 in 2 ways
Stage 3: Determine whether or not to place "u" in the subset We can either HAVE "u" in the subset or NOT HAVE "u" in the subset So, we can complete this stage in 2 ways
Stage 4: Determine whether or not to place "w" in the subset We can either HAVE "w" in the subset or NOT HAVE "w" in the subset So, we can complete this stage in 2 ways
Stage 5: Determine whether or not to place "x" in the subset We can complete this stage in 2 ways
By the Fundamental Counting Principle (FCP), we can complete the 5 stages (and thus build all possible subsets) in (1)(2)(2)(2)(2) ways (= 16 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: The subsets of the set {s, t, u} consisting of the three elements s, t
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01 Sep 2024, 20:59
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t [#permalink]