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How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d
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25 Oct 2021, 05:36
25 Oct 2021, 05:36
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How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12
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Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d
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25 Oct 2021, 06:09
25 Oct 2021, 06:09
Carcass wrote:
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12
Here's another approach:
Take the task of arranging the 5 digits and break it into stages.
Stage 1: Arrange the 4, 5 and 6
We can arrange n unique objects in n! ways
So, we can arrange these 3 digits in 3! ways (6 ways)
So, we can complete stage 1 in 6 ways
TRICKY PART: We'll now add some spaces where the 3's can be placed.
So, for example, if in stage 1, we arranged three digits as 645, then we'll add spaces before and after each digit.
So, we'd get: _6_4_5_
We will place the two 3's in two of the 4 possible spaces.
This will ENSURE that the 3's are not together.
Stage 2: Select two spaces in which to place the 3's
Since the order in which we select the spaces does not matter, we can use combinations.
We can select 2 spaces from 4 spaces in 4C2 ways (6 ways)
So, we can complete stage 2 in 6 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus arrange all 5 digits) in (6)(6) ways (= 36 ways)
Answer: B
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d [#permalink]
25 Oct 2021, 06:09
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