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Number of ways in which $A A A B B B$ can be placed in the squares of figure as shown so that no row remains empty is ?

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Permutation

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>Permutation

The largest non-negative integer

k

such that

24^{k}

divides

13!

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Mathematics>Algebra>Permutation and Combination>Permutation

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 :

HARD

Mathematics>Algebra>Permutation and Combination>Permutation

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>Permutation

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

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Mathematics>Algebra>Permutation and Combination>Permutation

In how many different ways can the letters of word CANDIDATE can be arranged in such a way that the vowels always come together?

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Mathematics>Algebra>Permutation and Combination>Permutation

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>Permutation

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>Permutation

{}^{56}{P_{r + 6}} : {}^{54}{P_{r + 3} = 30800 : 1}

,

then

r

is equal to

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Mathematics>Algebra>Permutation and Combination>Permutation

How many ways are there to arrange the letters of the word

EDUCATION

so that all the following three conditions hold?
- the vowels occur in the same order

(EUAIO),

- the consonants occur in the same order

(DCTN),

- no two consonants are next to each other.

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Mathematics>Algebra>Permutation and Combination>Permutation

The number of

4

letter words (with or without meaning) that can be formed from the eleven letters of the word

EXAMINATION

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Mathematics>Algebra>Permutation and Combination>Permutation

The total number of permutations of

n (> 1)

different things taken not more than

r

at a time, when each thing may be repeated any number of times is

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Mathematics>Algebra>Permutation and Combination>Permutation

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:

HARD

Mathematics>Algebra>Permutation and Combination>Permutation

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

EASY

Mathematics>Algebra>Permutation and Combination>Permutation

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:

HARD

Mathematics>Algebra>Permutation and Combination>Permutation

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>Permutation

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>Permutation

The number of distinct primes dividing

12! + 13! + 14!

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Mathematics>Algebra>Permutation and Combination>Permutation

How many natural numbers

n

are there such that

n! + 10

is a perfect square ?

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Mathematics>Algebra>Permutation and Combination>Permutation

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?

Number of ways in which AAABBB can be placed in the squares of figure as shown so that no row remains empty is ?

Important Questions on Permutation and Combination

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Number of ways in which $A A A B B B$ can be placed in the squares of figure as shown so that no row remains empty is ?