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A code word of length $4$ consists of two distinct consonants in the English alphabet followed by two digits from $1$ to $9$ , with repetition allowed in digits. If the number of code words, so formed ending with an even digit is $432 k$ , then $k$ is equal to

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Important Questions on Permutation and Combination

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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

{}^{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

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>Permutation

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutation

The largest non-negative integer

k

such that

24^{k}

divides

13!

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The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

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

EASY

Mathematics>Algebra>Permutation and Combination>Permutation

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>Permutation

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>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 :

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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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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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.

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

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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:

MEDIUM

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

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>Permutation

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>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)

A code word of length 4 consists of two distinct consonants in the English alphabet followed by two digits from 1 to 9, with repetition allowed in digits. If the number of code words, so formed ending with an even digit is 432k, then k is equal to

Important Questions on Permutation and Combination

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A code word of length $4$ consists of two distinct consonants in the English alphabet followed by two digits from $1$ to $9$ , with repetition allowed in digits. If the number of code words, so formed ending with an even digit is $432 k$ , then $k$ is equal to