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In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

How many numbers of four digits can be made by using the digits $3, 5, 6, 7,$ and $9$ ? (Repetition of digits is not allowed)

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The sum of the digits in the unit's place of all the

4

- digit numbers formed by using the numbers

3, 4, 5

and

6

, without repetition is :

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of

6

digit number that can be formed using the digits

0, 1, 2, 5, 7

and

9

which are divisible by

11

and no digit is repeated is:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If the number of all possible permutations of the letters of the word $M A T H E M A T I C S$ in which the repeated letters are not together is $90 (X)$ , then $X =$

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of ways in which

3

prizes can be distributed to

4

children, so that no child gets all the three prizes, are

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

From

6

different novels and

3

different dictionaries,

4

novels and

1

dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

{}^{n}P_{4} = 20 \times {}^{n}P_{2} .

Then, the value of

n

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated is

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all possible numbers are formed by using the digits

1, 2, 3, 5, 7

without repetition and they are arranged in descending order, then the rank of the number

327

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

A five-digit number divisible by

3

is to be formed using the numerals

0, 1, 2, 3, 4

and

5

without repetition. The total number of ways this can be done is

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

In a

12

storied building,

3

persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of four-letter words that can be formed with letters

a, b, c

such that all three letters occur is

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

A dictionary is printed consisting of

7

letters words only that can be made with a letters of word CRICKET. If the words are printed at the alphabetical order as in an ordinary dictionary, then the number of words before the word CRICKET is

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, then the

50^{th}

word will be

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of ways in which

5

girls and

3

boys can be seated in a row so that no two boys are together is

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of four-digit numbers strictly greater than

4321

that can be formed using the digit

0,1, 2,3, 4,5

(repetition of digits is allowed) is:

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

Important Questions on Permutation and Combination

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