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Find the number of numbers of five digits that can be made with the digits of the number $1203210$ .

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Important Questions on Permutation and Combination

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

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>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

4

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

EXAMINATION

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?

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

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

,

then

r

is equal to

EASY

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)

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

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>Permutations

The value of (

2 \cdot^{1} P_{0} - 3 \cdot^{2} P_{1} + 4 \cdot^{3} P_{2} - . . . . . . . .

up to

51^{th}

term)

+

(

1! - 2! + 3! - . . . . . . .

up to

51^{th}

term) is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

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.

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

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>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

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The number of words (with or without meaning) that can be formed from all the letters of the word

" L E T T E R "

in which vowels never come together is.....

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

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:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

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

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

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:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

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?

Find the number of numbers of five digits that can be made with the digits of the number 1203210.

Important Questions on Permutation and Combination

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Find the number of numbers of five digits that can be made with the digits of the number $1203210$ .