‘Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2’ is the topic for GMAT Quantitative Reasoning. GMAT quantitative reasoning section assesses the candidates' ability to solve mathematical, and quantitative problems and interpret graphic data. This section of the GMAT exam comprises 31 questions. This topic is the GMAT Quantitative Reasoning question. It includes five options and candidates need to choose one of them. Candidates are given 62 minutes to complete this section. GMAT Quant syllabus has mainly the two categories- Show
Topic: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
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Answer: C Model Answer 1 Explanation: considering the given question, what needs to be found is how many words can 3 consonants and 2 vowels out of 7 consonants and 4 vowels can be created. This implies that using 3 consonants and 2 vowels, 5-letter words are supposed to be created. Accordingly, how many words can be created by 5 letters needs to be evaluated focusing on 3 different stages. In
the first stage, it is needed to select the 3 consonants to work with The second stage states about selecting the 2 vowels to work with From here moving on
to stage three, 5 selected letters can be taken and arranged. With the need to find the number of words from 3 consonants and 2 vowels, the use of the Fundamental Counting Principle (FCP) can be ensured. Accordingly, by completing all the 3 stages the five letter words can be created in the following number of ways. It depicts the total number of ways that can be multiplied. This implies- (35)(6)(120) ways = 25,200 way Hence, option C with 25,200 ways is the correct answer. Model Answer 2 Explanation: With the given case of choosing 3 consonants out of 7 and two vowels out of 4, the number of words that can be formed would include five letters. Accordingly, the positions or arrangement of the letters is not mentioned which means, it can be in any way. For this, the following evaluations need to be considered to find the total number of words. For the five-letter words with 3 consonants, the number of ways where these can be used in terms of 3 positions can be equated with the combination of 5C3. This can be equated as- \(\frac{5*4*3}{3*2*1}=10\) For the remaining 2 positions in the 5 letter words, where the 2 positions would be used by the 2 vowels, the combination that can be identified is 2C2. This can be equated as- \(\frac{2*1}{2*1}=1\) Number of
options for the first consonant = 7, which can be any of the 7 consonants By combining all of these options that have been found from above, all of these values need to be multiplied. This would stand as- 10*1*7*6*5*4*3 = 25,200 Hence, the number of words that can be formed out of 3 consonants and 2 vowels is 25,200 which is the right option for C. How many words of 4 consonants and 4 vowels can be formed out of 8 vowels and 5 Consonents?Detailed Solution
But all these five alphabets can permute among themselves = 5! ∴ The required result will be 40320.
How many words can be formed out of 5 different consonants and 4 different vowels if each word is to contain 3 consonant and 2 vowels?D. 7200. Hint: The number of ways a word can form from $5$ consonants by using $3$ consonants $ = $ ${}^5{C_3}$ and from $4$ vowels by using $2$ vowels $ = $${}^4{C_2}$, hence the number of words can be $ = {}^5{C_3} \times {}^4{C_2} \times {}^5{P_5}$.
How many words of 2 consonants and 2 vowels can be formed from 5 consonants and 4 vowels?⇒ Number of ways selecting 2 consonants = (5 × 4 × 3!)/(2 × 1 × 3!) ∴ The total number of ways is 1440.
How many words of 4 consonants and 2 vowels can be formed out of 6 consonants and 3 vowels?Answer: (2) 756000
= 6C4 x 5C3 x 7!
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