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

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Important Questions on Counting Principles

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Aptitude>Arithmetic>Counting Principles>Combinations

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

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Aptitude>Arithmetic>Counting Principles>Combinations

The number of integers greater than

6000

that can be formed, using the digits

3, 5, 6, 7

and

8

, without repetition is

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Aptitude>Arithmetic>Counting Principles>Combinations

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:

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Aptitude>Arithmetic>Counting Principles>Combinations

The number of integers

n

with

100 \leq n \leq 999

and containing at most two distinct digits is

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

The value of

{}^{16}C_{9} + {}^{16}C_{10} - {}^{16}C_{6} - {}^{16}C_{7}

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

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

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

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

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

A committee of five members is to be formed out of

3

trainees,

4

professors and

6

research associates. In how many different ways can this be done if the committee should have all the

4

professors and

1

research associate or all

3

trainees and

2

professors?

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Aptitude>Arithmetic>Counting Principles>Combinations

The number of selection of

n

objects from

2 n

objects of which

n

are identical and the rest are different, is

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Aptitude>Arithmetic>Counting Principles>Combinations

In order to get through in an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails. The number of ways in which he can fail, in this examination is

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Aptitude>Arithmetic>Counting Principles>Combinations

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,

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

Total number of

6

-digit numbers in which only and all the five digits

1, 3, 5, 7

and

9

appears, is

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

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-

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Aptitude>Arithmetic>Counting Principles>Combinations

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

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Aptitude>Arithmetic>Counting Principles>Combinations

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 :

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Aptitude>Arithmetic>Counting Principles>Combinations

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

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

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:

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Aptitude>Arithmetic>Counting Principles>Combinations

Let

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

where

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

and

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots (C_{n - 1} + C_{n}) = A C_{1} C_{2} \dots C_{n}

, then for

n = 5, A

is equal to

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

In how many ways a team of $5$ members can be chosen from $8$ members?

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Aptitude>Arithmetic>Counting Principles>Combinations

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is

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

Important Questions on Counting Principles

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