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The number of ways in which $9$ things can be divided into twice groups containing $2, 3,$ and $4$ things respectively is_______

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Permutations

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>Permutations

How many number divisible by

5

6

digit can be made from the digit

2, 3, 4, 5, 6, 7

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

The number of ways in which

3

prizes can be distributed to

4

children, so that no child gets all the three prizes, are

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The number of (a, b, c), where a, b, c are positive integers such that $abc = 30$ , is

MEDIUM

Mathematics>Algebra>Permutation and Combination>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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Mathematics>Algebra>Permutation and Combination>Permutations

{}^{n}P_{4} = 20^{n} P_{2}

where

P

denotes the number of permutations, then

n =

________

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Mathematics>Algebra>Permutation and Combination>Permutations

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

, then

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

{}^{n}P_{5} : {}^{n}P_{3}

2 : 1

than value of

n

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

{}^{n}p_{6} = 20 {}^{n}p_{4}

then the value of

n

is given by

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

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

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

{}^{n}P_{r} = 840

and

{}^{n}C_{r} = 35

, then the value of

r

is equal to

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

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

,

then

r

is equal to

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

A five-digit number divisible by

3

is to be formed using the numerals

0, 1, 2, 3, 4

and

5

without repetition. The total number of ways this can be done is

MEDIUM

Mathematics>Algebra>Permutation and Combination>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?

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Mathematics>Algebra>Permutation and Combination>Permutations

a, b, c

are three particular speakers among the

10

speakers of a meeting. The number of ways of arranging all the

10

speakers on the dias in a row so that all the three speakers

a, b, c

do not sit together is

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Mathematics>Algebra>Permutation and Combination>Permutations

5

boys and

3

girls are to be seated together such that no two girls are together

EASY

Mathematics>Algebra>Permutation and Combination>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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Mathematics>Algebra>Permutation and Combination>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)

The number of ways in which 9 things can be divided into twice groups containing 2,3,and 4 things respectively is_______

Important Questions on Permutation and Combination

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The number of ways in which $9$ things can be divided into twice groups containing $2, 3,$ and $4$ things respectively is_______