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Runners V, W, X, Y, and Z are competing in the Bayville local triathlo
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05 Oct 2021, 10:00
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Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??
Re: Runners V, W, X, Y, and Z are competing in the Bayville local triathlo
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05 Oct 2021, 10:12
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Carcass wrote:
Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??
A. 5 B. 10 C. 30 D. 60 E. 120
Take the task of arranging the 5 runners and break it into stages.
GIVEN: V finishes before W and W finishes before Z So, the order is: Z - W - V Our goal is to now place the remaining 2 runners (runner X and runner Y)
NOTE: I'm going to IGNORE the restriction that says X must finish before Y You'll see why shortly.
Stage 1: place runner X into the existing order. Notice that if we already have the arrangement Z - W - V, then we can place spaces in the areas where runner X might go. We have: _Z_W_V_ Since there are 4 spaces where we can place runner X, we can complete stage 1 in 4 ways
Stage 2: place runner Y into the existing order. At this point, we have placed runners Z, W, V and X Let's pretend for a moment, that the arrangement is ZXWV From here, we can place spaces in the areas where runner Y might go. We have: _Z_X_W_V_ Since there are 5 spaces where we can place runner Y, we can complete stage 2 in 5 ways
By the Fundamental Counting Principle (FCP), we can the 2 stages (and thus arrange all 5 runners) in (4)(5) ways (= 20 ways)
IMPORTANT: If we IGNORE the restriction that says X must finish before Y, then there are 20 possible arrangements. However, in HALF of those 20 arrangements, X is ahead of Y, and in the other HALF of those 20 arrangements, Y is ahead of X.
So, the number of arrangements in which X is ahead of Y = 20/2 = 10
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: Runners V, W, X, Y, and Z are competing in the Bayville local triathlo
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13 Jan 2023, 10:44
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Re: Runners V, W, X, Y, and Z are competing in the Bayville local triathlo [#permalink]