How many words, with or without meaning, each of 2 vowels and 3 consonants
can be formed from the letters of the word DAUGHTER ?
Last updated date: 26th Mar 2023
•
Total views: 309.3k
•
Views today: 6.86k
Answer
309.3k+ views
Hint:- Find, total number of vowels and consonants in the given word.
As we know that in English alphabets A, E, I, O and U are vowels.
And the rest of the alphabets are consonants.
So, we can see that in the word DAUGHTER.
\[ \Rightarrow \]Total number of letters are 8. In which,
\[ \Rightarrow \]Total vowels \[ = {\text{ }}3\]
\[ \Rightarrow \]Total consonants \[ = 5\]
Now, we had to make a word using five letters of the given word.
Out of the five letters 2 should be vowels and 3 should be consonants.
\[ \Rightarrow \]So, here we had to choose 2 vowels out of the 3 vowels,
And that will be done in \[{}^3{C_2}\]\[{\text{ = 3 }}\]ways.
\[ \Rightarrow \]And 3 consonants out of 5 consonants.
And that will be done in \[{}^5{C_3}{\text{ = 10 }}\]ways.
\[ \Rightarrow \]And then arrange that five letters of word in \[5!\] ways.
So, total number of ways of forming a five letters word from the given word
DAUGHTER having 2 vowels and 3 consonants will be;
\[ \Rightarrow \]Total ways \[ = {}^3{C_2}*{}^5{C_3}*5! = 3600\].
Note:- Whenever we came up with this type of problems then first, we should
find the number of ways for selection of vowels and then find number of ways
for the selection of consonants. And at last never forget to multiply the number
of ways by \[n!\] to get the total number of ways. As it is given in the question that
a word of five letters can also be meaningless.
As we know that in English alphabets A, E, I, O and U are vowels.
And the rest of the alphabets are consonants.
So, we can see that in the word DAUGHTER.
\[ \Rightarrow \]Total number of letters are 8. In which,
\[ \Rightarrow \]Total vowels \[ = {\text{ }}3\]
\[ \Rightarrow \]Total consonants \[ = 5\]
Now, we had to make a word using five letters of the given word.
Out of the five letters 2 should be vowels and 3 should be consonants.
\[ \Rightarrow \]So, here we had to choose 2 vowels out of the 3 vowels,
And that will be done in \[{}^3{C_2}\]\[{\text{ = 3 }}\]ways.
\[ \Rightarrow \]And 3 consonants out of 5 consonants.
And that will be done in \[{}^5{C_3}{\text{ = 10 }}\]ways.
\[ \Rightarrow \]And then arrange that five letters of word in \[5!\] ways.
So, total number of ways of forming a five letters word from the given word
DAUGHTER having 2 vowels and 3 consonants will be;
\[ \Rightarrow \]Total ways \[ = {}^3{C_2}*{}^5{C_3}*5! = 3600\].
Note:- Whenever we came up with this type of problems then first, we should
find the number of ways for selection of vowels and then find number of ways
for the selection of consonants. And at last never forget to multiply the number
of ways by \[n!\] to get the total number of ways. As it is given in the question that
a word of five letters can also be meaningless.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
