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A box contains $2$ white balls, $3$ black balls, and $4$ red. In how many ways can $3$ balls be drawn from the box if at least one black ball is to be included in the draw?

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Important Questions on Permutations, Combinations and Probability

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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

HARD

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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-

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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:

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

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

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

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

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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?

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

The number of times the digit

7

will be written when listing the integers from

1

1000

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

The number of integers

n

with

100 \leq n \leq 999

and containing at most two distinct digits is

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

The number of ways of dividing

15

men and

15

women into

15

couples, each consisting of man and woman is

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

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

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

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

HARD

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

Consider a rectangle

A B C D

having

5, 6, 7, 9

points in the interior of the line segments

A B, B C, C D, D A

respectively. Let

α

be the number of triangles having these points from different sides as vertices and

β

be the number of quadrilaterals having these points from different sides as vertices. Then

(β - α)

is equal to

EASY

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

The number of all positive odd divisors of

17500

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

The sum of all proper divisor of

9900

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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,

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and 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

MEDIUM

Quantitative Aptitude>Arithmetic>Permutations, Combinations and Probability>Permutations and Combinations

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 :

A box contains 2 white balls, 3 black balls, and 4 red. In how many ways can 3 balls be drawn from the box if at least one black ball is to be included in the draw?

Important Questions on Permutations, Combinations and Probability

Learn and Prepare for any exam you want !

A box contains $2$ white balls, $3$ black balls, and $4$ red. In how many ways can $3$ balls be drawn from the box if at least one black ball is to be included in the draw?