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Each participant in a certain study was assigned a sequence
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01 Apr 2020, 09:29
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20% (01:47) wrong based on 25 sessions
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Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
Each participant in a certain study was assigned a sequence
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01 Apr 2020, 09:45
Expert Reply
Carcass wrote:
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
A 20
B 92
C 300
D 372
E 476
Kudos for the right answer and explanation
Take the task of creating sequences and break it into stages.
Stage 1: Select the first letter of the sequence There are 8 letters to choose from. So, we can complete stage 1 in 8 ways
Stage 2: Select the second letter of the sequence There are 7 REMAINING letters to choose from (since the three letters must be different). So, we can complete stage 2 in 7 ways
Stage 3: Select the last letter of the sequence There are 6 REMAINING letters to choose from. So, we can complete stage 3 in 6 ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a sequence) in (8)(7)(6) ways (= 336 ways) This means we are able to create enough sequences to accommodate 336 participants in the study. Since 36 of the possible sequences were not assigned, the number of participants = 336 - 36 = 300
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.