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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these?
Most Upvoted Answer
The number of different words that can be formed with 12 consonants an...
Solution:
Given, we have 12 consonants and 5 vowels.
We need to form a word with 4 consonants and 3 vowels.
We need to find the number of different words that can be formed with given conditions.
Let's solve the problem step by step.
Step 1: Find the number of ways to select 4 consonants from 12 consonants
Number of ways to select 4 consonants from 12 consonants = 12C4 = (12!)/(4!*(12-4)!) = 495
Step 2: Find the number of ways to select 3 vowels from 5 vowels
Number of ways to select 3 vowels from 5 vowels = 5C3 = (5!)/(3!*(5-3)!) = 10
Step 3: Find the number of ways to arrange 4 selected consonants and 3 selected vowels
The number of ways to arrange n distinct objects is n!
Number of ways to arrange 4 consonants = 4!
Number of ways to arrange 3 vowels = 3!
Number of ways to arrange 4 selected consonants and 3 selected vowels = 4!*3! = 24
Step 4: Find the total number of different words that can be formed
Number of different words that can be formed = (Number of ways to select 4 consonants from 12 consonants) * (Number of ways to select 3 vowels from 5 vowels) * (Number of ways to arrange 4 selected consonants and 3 selected vowels)
Number of different words that can be formed = 495 * 10 * 24 = 118800
Hence, the number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is 118800.
Therefore, the correct option is d) none of these.
Given, we have 12 consonants and 5 vowels.
We need to form a word with 4 consonants and 3 vowels.
We need to find the number of different words that can be formed with given conditions.
Let's solve the problem step by step.
Step 1: Find the number of ways to select 4 consonants from 12 consonants
Number of ways to select 4 consonants from 12 consonants = 12C4 = (12!)/(4!*(12-4)!) = 495
Step 2: Find the number of ways to select 3 vowels from 5 vowels
Number of ways to select 3 vowels from 5 vowels = 5C3 = (5!)/(3!*(5-3)!) = 10
Step 3: Find the number of ways to arrange 4 selected consonants and 3 selected vowels
The number of ways to arrange n distinct objects is n!
Number of ways to arrange 4 consonants = 4!
Number of ways to arrange 3 vowels = 3!
Number of ways to arrange 4 selected consonants and 3 selected vowels = 4!*3! = 24
Step 4: Find the total number of different words that can be formed
Number of different words that can be formed = (Number of ways to select 4 consonants from 12 consonants) * (Number of ways to select 3 vowels from 5 vowels) * (Number of ways to arrange 4 selected consonants and 3 selected vowels)
Number of different words that can be formed = 495 * 10 * 24 = 118800
Hence, the number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is 118800.
Therefore, the correct option is d) none of these.
Community Answer
The number of different words that can be formed with 12 consonants an...
The answer is c)
selection of 4consonants from 12 =12C4
selection of 3 vowels from 5 =5C3
the 7 letters(4 consonants and 3 vowels ) arrange themeselves ammong themselves in 7! ways
the total no.of ways = 12C4×5C3×7!
= 4950 ×7!
selection of 4consonants from 12 =12C4
selection of 3 vowels from 5 =5C3
the 7 letters(4 consonants and 3 vowels ) arrange themeselves ammong themselves in 7! ways
the total no.of ways = 12C4×5C3×7!
= 4950 ×7!
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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these?
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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these?.
The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is a) 12C4 × 5C3 b) 17C7 c) 4950 × |_7! d) none of these?.
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