nphilli1
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
*Question edited: 09/10/2016 and OA added.
I got 476, the answer given was 300
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 GMAT. So, be sure to learn it.
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