
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
None of these
Answer
489.9k+ views
1 likes
Hint: There are letters in the word ‘MATHEMATICS’,
We have to find the number of ways of arranging these letters
Also the given number of letters out of which there are vowels.
Here, we have to apply the concept of permutation to solve the question.
Finally we get the required answer.
Formula used:
Complete step-by-step answer:
As per the question the word ‘Mathematics’ consists of total letters, out of which distinct vowels are present.
So we have as consonants and as vowels.
Now we have to arrange letters, occurs two times and occurs two times and others are different.
Therefore, the number of ways of arranging these letters
On splitting the factorial we get,
On multiplying the term we get,
Now, we have letters as vowels in the word ‘Mathematics’. The vowel occurs two times and others are distinct.
Here and
Number of ways of arranging these letters
On subtracting the bracket term we get,
The total required number of ways
On multiplying the terms we get
Thus the correct option is
Note: In general, permutation can be defined as the act of arranging all the members of a group in an order or sequence. We can also say that if the group is already arranged, then rearranging of the members is known as the procedure of permuting.
Permutation takes place in almost all areas of mathematics. It is specifically used where the order of the data matters.
Combination can be defined as the technique of selecting things from a collection in such a manner that the order of selection does not matter. It is generally used where the order of data does not matter.
We have to find the number of ways of arranging these letters
Also the given number of letters out of which there are
Here, we have to apply the concept of permutation to solve the question.
Finally we get the required answer.
Formula used:
Complete step-by-step answer:
As per the question the word ‘Mathematics’ consists of total
So we have
Now we have to arrange
Therefore, the number of ways of arranging these letters
On splitting the factorial we get,
On multiplying the term we get,
Now, we have
Here
Number of ways of arranging these letters
On subtracting the bracket term we get,
The total required number of ways
On multiplying the terms we get
Thus the correct option is
Note: In general, permutation can be defined as the act of arranging all the members of a group in an order or sequence. We can also say that if the group is already arranged, then rearranging of the members is known as the procedure of permuting.
Permutation takes place in almost all areas of mathematics. It is specifically used where the order of the data matters.
Combination can be defined as the technique of selecting things from a collection in such a manner that the order of selection does not matter. It is generally used where the order of data does not matter.
Latest Vedantu courses for you
Grade 7 | CBSE | SCHOOL | English
Vedantu 7 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹42,500 per year
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
State and prove Bernoullis theorem class 11 physics CBSE

What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

Who built the Grand Trunk Road AChandragupta Maurya class 11 social science CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

State the laws of reflection of light
