How many words consisting of 4 consonants and 3 vowels can be formed out?
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There are 3 consonants and 3 vowels. Show
= `((8 xx 7 xx 6 xx 5))/((4 xx 3 xx 2)) xx ((3 xx 2 xx 1))/((2 xx 1)` = 70 × 3 Note: In this question, students must take care that here the vowels as well as the consonants are repeating in nature as the word ‘DIFFERENTIATION” has more than one similar vowels and consonants and so we need to apply the arrangement in that also. So I am having some trouble with a few parts of my homework problem. The question gives us 3 vowels (A,E,O) and 4 consonants (B,C,D,F). a) How many ways can you make a 7 letter word if each letter can only be used once. (Word doesn't have to be real). This was easy, as the answer is just 7! b) If the vowels have to be together and the consonants have to be together? My approach: 3 vowels can be rearranged in 3! ways and 4 consonants in 4! ways, and the vowels can be leading or ending, so the total is 3! * 4! * 2!. c) If the vowels have to be together? My approach: 3 vowels in 3! ways, and can be rearranged in 5! ways. d) If B and C have to be together, but no other vowels or consonants can be together? My approach: I first tried making a word that starts with a consonant, and then alternating between vowel and consonant, while keeping B and C last. My other word started with a vowel then a consonant, then B and C, then vowel, consonant and the vowel. This is all I could think of, and I'm not sure how the math checks out on this. Solution(By Examveda Team)4 consonants out of 12 can be selected in,12C4 ways. 3 vowels can be selected in 4C3 ways. Therefore, total number of groups each containing 4 consonants and 3 vowels, = 12C4 × 4C3 Each group contains 7 letters, which can be arranging in 7! ways. Therefore required number of words, = 12C4 × 4C3 × 7! How many words of 4 consonants and 3 vowels can be?∴ Required number of words =12C4∗4C3∗7! =9979200.
How many words of 4 consonants and 3 vowels can be formed out of 8 consonants and 5 vowels?Out of 8 consonants and 5 vowels, how many words can be made, each containing 4 consonants and 3 vowels? Internal arrangement of 7 letters = 7! Hence, option C is the correct answer.
How many words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels if all the letters are different?Explanation: There are 4 consonants out of 15 can be selected in 15C4 ways and 3 vowels can be selected in 5C3 ways. Therefore, the total number of groups each containing 4 consonants and 3 vowels = 15C4 * 4C3. Each group contains 7 letters which can be arranged in 7! ways.
How many words of 4 consonants and 3 vowels can be formed from 12 consonants and 4 vowels if all letters are different?12C4 ways. 3 vowels can be selected in 4C3 ways. Therefore, total number of groups each containing 4 consonants and 3 vowels, = 12C4 *4C3 Each group contains 7 letters, which can be arranging in 7!
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