HARD

Earn 100

Let $X$ be the set of all $6 -$ digit numbers, where all the digits of each number are from the set ${1, 2, 3, 4, 5}$ , and any digit that appears in any one of the numbers appears at least twice (in the same number). Then the number of distinct elements in the set $X$ equals

50% studentsanswered this correctly

Important Questions on Permutations and Combinations

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

HARD

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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 $X =$

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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

HARD

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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>Permutations and Combinations>Permutations of Alike Things and Repeated Things

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations of Alike Things and Repeated Things

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?

Let X be the set of all 6-digit numbers, where all the digits of each number are from the set {1,2,3,4,5}, and any digit that appears in any one of the numbers appears at least twice (in the same number). Then the number of distinct elements in the set X equals

Important Questions on Permutations and Combinations

Learn and Prepare for any exam you want !

Let $X$ be the set of all $6 -$ digit numbers, where all the digits of each number are from the set ${1, 2, 3, 4, 5}$ , and any digit that appears in any one of the numbers appears at least twice (in the same number). Then the number of distinct elements in the set $X$ equals