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How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$ , if each number starts with $67$ and no digit appears more than once?

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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

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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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

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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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

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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:

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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

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

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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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:

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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:

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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:

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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

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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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

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

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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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)

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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 :

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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?

How many 5 digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?

Important Questions on Permutation and Combination

Learn and Prepare for any exam you want !

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$ , if each number starts with $67$ and no digit appears more than once?