How many words can be formed each of 2 vowels and 3 consonants from the word daughter?

Solution :  The given word 'DAUGHTER' contains 3 vowels and 5 consonants. Total number of ways of choosing
[2 vowels out of 3 ] and [3 consonants out of 5]
`=[.^[3]C_[2]xx.^[5]C_[3]]=[.^[3]C_[1]xx.^[5]C_[2]]=[3xx[5xx4]/[2xx1]]=30`.
Number of groups, each containing 2 vowels and 3 consonants=30.
Each group contains 5 letters.
Number of ways of arranging 5 letters amongst themselves
`=5! =[5xx4xx3xx2xx1]=120`.
Hence, the required number of words`=[30xx120]=3600`.

Indus question we have to choose two hours and consonant from the letters of word daughter and we have to find it in how many words we can make by using two hours and 3 consonants so in word consonant we have one De 1A 1u 1GB 1h 1t 1e and one hour so we have all different letter this 8 letter how many hours this is mobile Evil you is evil

and is over and how many consonants here is consonant G consonant letters consonant please consonant and vowel consonant 35 sothi bubble message to bhabhi choose karne ke bich kitne Honge 3 C2 first counselling dates message free concert use karne ke liye kitne Honge 52 suit total number of formations Kitni Hogi 3 consonant this is 35 C3 because you to choose three consonant total number of formation kitne hue total is equal to

3C 225 C3 it is equal to 3 into 5 into 4 upon 2 is equal to 3 into 10 30 30 number of possible combinations of two vowels and 3 consonants and we know he is combination memory five different letter use karen to 15 different letters were arranged kaise kar sakte ho sakta Railway se total possible words on total possible word meaning Phool aur meaningless total possible words equal to 5 factorial

in 235 factorial is equal to 120 into 32223 36 total number of vedar 3600

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

In the word DAUGHTER, there are 3 vowels namely, A, U, and E, and 5 consonants namely, D, G, H, T, and R.

Number of ways of selecting 2 vowels out of 3 vowels =`""^3C_2 = 3`

Number of ways of selecting 3 consonants out of 5 consonants = `""^5C_2 = 3`

Therefore, number of combinations of 2 vowels and 3 consonants = 3 × 10 = 30

Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways.

Hence, required number of different words = 30 × 5! = 3600

In the word DAUGHTER, there are 3 vowels namely, A, U, and E, and 5 consonants namely, D, G, H, T, and R.

Number of ways of selecting 2 vowels out of 3 vowels =`""^3C_2 = 3`

Number of ways of selecting 3 consonants out of 5 consonants = `""^5C_2 = 3`

Therefore, number of combinations of 2 vowels and 3 consonants = 3 × 10 = 30

Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways.

Hence, required number of different words = 30 × 5! = 3600

Concept: Combination

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Solution

There are 8 letters in the word DAUGHTER including 3 vowels and 5 consonants. We have to select 2 vowels out of 3 vowels and 3 consonants out of 5 consonants.

∴ Number of ways of selection = 3C2×5C3=3×10=30

Now each word contains 5 letters which can be arranged among themselves in 5! ways. So, total number of words
= 5!×30=120×30=3600.

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