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The number of ways in which $4$ boys and $4$ girls can sit alternatively in a row if a particular boy and a particular girl are never adjacent to each other, are

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Important Questions on Counting Principles

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Aptitude>Arithmetic>Counting Principles>Permutations

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

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Aptitude>Arithmetic>Counting Principles>Permutations

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

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Aptitude>Arithmetic>Counting Principles>Permutations

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 $X =$

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Aptitude>Arithmetic>Counting Principles>Permutations

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

Then, the value of

n

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Aptitude>Arithmetic>Counting Principles>Permutations

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:

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Aptitude>Arithmetic>Counting Principles>Permutations

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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Aptitude>Arithmetic>Counting Principles>Permutations

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

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Aptitude>Arithmetic>Counting Principles>Permutations

In a group of

8

girls, two girls are sisters. The number of ways in which the girls can sit so that the two sisters are not sitting together is

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Aptitude>Arithmetic>Counting Principles>Permutations

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:

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Aptitude>Arithmetic>Counting Principles>Permutations

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:

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Aptitude>Arithmetic>Counting Principles>Permutations

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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Aptitude>Arithmetic>Counting Principles>Permutations

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:

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Aptitude>Arithmetic>Counting Principles>Permutations

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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Aptitude>Arithmetic>Counting Principles>Permutations

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?

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Aptitude>Arithmetic>Counting Principles>Permutations

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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Aptitude>Arithmetic>Counting Principles>Permutations

There are

m

books in black cover and

n

books in blue cover, and all books are different. The number of ways these

(m + n)

books can be arranged on a shelf so that all the book in black cover are put side by side is

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Aptitude>Arithmetic>Counting Principles>Permutations

5

boys of class

VI

6

boys of class

VII

and

7

boys of class

VIII

sit in a row. The number of ways they can sit so that boys of the same class sit together is

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Aptitude>Arithmetic>Counting Principles>Permutations

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)

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Aptitude>Arithmetic>Counting Principles>Permutations

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 :

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Aptitude>Arithmetic>Counting Principles>Permutations

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?

The number of ways in which 4 boys and 4 girls can sit alternatively in a row if a particular boy and a particular girl are never adjacent to each other, are

Important Questions on Counting Principles

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The number of ways in which $4$ boys and $4$ girls can sit alternatively in a row if a particular boy and a particular girl are never adjacent to each other, are