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Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
[#permalink]
25 Oct 2021, 06:07
Carcass wrote:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 210 B. 1050 C. 25200 D. 21400 E. 42800
Take the task of creating 5-letter words and break it into stages.
Stage 1: Select the 3 consonants to work with Since the order in which we select the consonants does not matter, we can use combinations. We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)
Stage 2: Select the 2 vowels to work with Since the order in which we select the vowels does not matter, we can use combinations. We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)
If anyone is interested, we have a video on calculating combinations (like 4C2) in your head - see below
Stage 3: Take the 5 selected letters and arrange them. We can complete this stage in 5! ways (= 120 ways).
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25,200 ways)
Answer: C
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: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink]