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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 × 5 c3 (b) 17c 7 (c) 4950 × 7! (d) none of these?
Most Upvoted Answer
The number of different words that can be formed with 12 consonants an...
12 consonants and 5 vowels
~ Taking 4 consonants and 3 vowels in each word
= 12C4 X 5C3
= 495 X 10
= 4950
Now 4950 words can also be arranged.
~ So these words can be arranged in 7! ways
= 4950 X 7!
Answer = (c) 4950 X 7!
~ Taking 4 consonants and 3 vowels in each word
= 12C4 X 5C3
= 495 X 10
= 4950
Now 4950 words can also be arranged.
~ So these words can be arranged in 7! ways
= 4950 X 7!
Answer = (c) 4950 X 7!
Community Answer
The number of different words that can be formed with 12 consonants an...
Question Analysis:
We are given 12 consonants and 5 vowels, and we need to find the number of different words that can be formed by taking 4 consonants and 3 vowels in each word. We have to determine the correct option from the given choices.
Solution:
To solve this problem, we can use the concept of combinations.
Step 1: Determine the number of ways to choose 4 consonants from 12.
The number of ways to choose 4 consonants from 12 can be found using the combination formula.
12c4 = 12! / (4! * (12-4)!)
= 12! / (4! * 8!)
= (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
= 495
Step 2: Determine the number of ways to choose 3 vowels from 5.
Similarly, the number of ways to choose 3 vowels from 5 can be found using the combination formula.
5c3 = 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4) / (2 * 1)
= 10
Step 3: Determine the total number of different words.
Since we need to choose 4 consonants and 3 vowels for each word, the total number of different words can be found by multiplying the number of ways to choose consonants and vowels.
Total number of different words = 495 * 10
= 4950
Therefore, the correct option is (c) 4950 × 7!
We are given 12 consonants and 5 vowels, and we need to find the number of different words that can be formed by taking 4 consonants and 3 vowels in each word. We have to determine the correct option from the given choices.
Solution:
To solve this problem, we can use the concept of combinations.
Step 1: Determine the number of ways to choose 4 consonants from 12.
The number of ways to choose 4 consonants from 12 can be found using the combination formula.
12c4 = 12! / (4! * (12-4)!)
= 12! / (4! * 8!)
= (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
= 495
Step 2: Determine the number of ways to choose 3 vowels from 5.
Similarly, the number of ways to choose 3 vowels from 5 can be found using the combination formula.
5c3 = 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4) / (2 * 1)
= 10
Step 3: Determine the total number of different words.
Since we need to choose 4 consonants and 3 vowels for each word, the total number of different words can be found by multiplying the number of ways to choose consonants and vowels.
Total number of different words = 495 * 10
= 4950
Therefore, the correct option is (c) 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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (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 × 5 c3 (b) 17c 7 (c) 4950 × 7! (d) none of these?.
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