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How many numbers between $3000$ and $5000$ divisible by 5 can be made using the digits $0, 4, 3 . 2 . 5 ?$

Important Questions on Permutation and Combination

HARD

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

An urn contains

5

red marbles,

4

black marbles and

3

white marbles. Then, the number of ways in which

4

marbles can be drawn so that at the most three of them are red is ___________.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Let

S = \{(a, b) : a, b \in Z, 0 \leq a, b \leq 18\} .

The number of elements

(x, y)

S

such that

3 x + 4 y + 5

is divisible by

19

is,

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is

R

and the fourth letter is

E

, then the total number of all such words is :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

n

-digit numbers are formed using only three digits

2, 5

and

7

. The smallest value of

n

for which

900

such distinct numbers can be formed is :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of numbers between

2, 000

and

5, 000

that can be formed with the digits

0, 1, 2, 3, 4

(repetition of digits is not allowed) and are multiple of

3

EASY

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

If the number of five digit numbers with distinct digits and

2

at the

10^{t h}

place is

336 k

, then

k

is equal to:

HARD

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Let

S = \{(a, b)| a, b \in Z, 0 \leq a, b \leq 18\}

. The number of lines in

R^{2}

passing through

(0, 0)

and exactly one other point in

S

is-

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

A five-digit number divisible by

3

is to be formed using the numbers

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>Fundamental Principles of Counting

Ten points lie in a plane so that no three of them are collinear. The number of lines passing through exactly two of these points and dividing the plane into two regions each containing four of the remaining points is

EASY

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

S

is a set with

10

elements and

A = \{(x, y) : x, y \in S, x \neq y\}

,

then the number of elements in

A

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Five points are marked on a circle. The number of distinct polygons of three or more sides can be drawn using some (or all) of the five points as vertices is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of natural numbers less than

7000

which can be formed by using the digits

0, 1, 3, 7, 9

(repetition of digits allowed) is equal to:

EASY

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Let

S = {0, 1, 2, 3, \dots, 100}

. The number of ways of selecting

x, y \in S

such that

x \neq y

and

x + y = 100

EASY

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Let

M = \{(a_{1}, a_{2}, a_{3}) : a_{i} \in \{1, 2, 3, 4\}, a_{1} + a_{2} + a_{3} = 6\} .

Then the number of elements in

M

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

Let

m

(respectively,

n

) be the number of

5

-digit integers obtained by using the digits

1, 2, 3, 4, 5

with repetitions (respectively, without repetitions) such that the sum of any two adjacent digits is odd. Then

\frac{m}{n}

is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The chairs at an auditorium are to be labelled with a letter and a positive integer not exceeding

100

. The largest number of chairs that can be marked differently is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of ways of dividing

15

men and

15

women into

15

couples, each consisting of man and woman is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of integers

n

with

100 \leq n \leq 999

and containing at most two distinct digits is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of

5

digit numbers which are divisible by

4

, with digits from the set

{1,2, 3,4, 5}

and the repetition of digits is allowed, is _____.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Fundamental Principles of Counting

The number of integers greater than

6000

that can be formed, using the digits

3, 5, 6, 7

and

8

, without repetition is

How many numbers between 3000 and 5000 divisible by 5 can be made using the digits 0, 4, 3. 2. 5?

Important Questions on Permutation and Combination

Learn and Prepare for any exam you want !

How many numbers between $3000$ and $5000$ divisible by 5 can be made using the digits $0, 4, 3 . 2 . 5 ?$