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m distinct animals of a circus have to be placed in m cages, one in each cage. If $n (< m)$ cages are too small to accommodate $p (n < p < m)$ animals, then the number of ways of putting the animals into cages are

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Important Questions on Permutation and Combination

HARD

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

The number of

4

digit numbers without repetition that can be formed using the digits

1, 2, 3, 4, 5, 6, 7

in which each number has two odd digits and two even digits 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

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

HARD

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

There are

10

red and

5

yellow roses of different sizes. If

x

is the number of garlands that can be formed with all these flowers so that no two yellow roses come together and

y

is the number of garlands formed with all these flowers so that all the red roses coming together, then

\frac{2 (x - y)}{10!} =

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

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

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

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

Then, the value of

n

HARD

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

If all the words (with or without meaning) having five letters, formed using the letters of the word

S M A L L

and arranged as in a dictionary; then the position of the word

S M A L L

HARD

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

All possible numbers are formed using the digits

1, 1, 2, 2, 2, 2, 3, 4, 4

taken all at a time. The number of such numbers in which the odd digits occupy even places is

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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

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

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

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

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

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:

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 :

MEDIUM

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?

m distinct animals of a circus have to be placed in m cages, one in each cage. If n <m cages are too small to accommodate pn<p<m animals, then the number of ways of putting the animals into cages are

Important Questions on Permutation and Combination

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m distinct animals of a circus have to be placed in m cages, one in each cage. If $n (< m)$ cages are too small to accommodate $p (n < p < m)$ animals, then the number of ways of putting the animals into cages are