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There are $15$ points in a plane out of which $6$ are collinear. Find the number of lines that can be formed from $15$ points.

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Important Questions on Counting Principles

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

How many number divisible by

5

6

digit can be made from the digit

2, 3, 4, 5, 6, 7

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

{}^{n}P_{r} = 840

and

{}^{n}C_{r} = 35

, then the value of

r

is equal to

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

The number of (a, b, c), where a, b, c are positive integers such that $abc = 30$ , is

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

{{}^{n}C}_{r - 1} = 36, {{}^{n}C}_{r} = 84

and

{{}^{n}C}_{r + 1} = 126

,

then

n =

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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:

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

a, b, c

are three particular speakers among the

10

speakers of a meeting. The number of ways of arranging all the

10

speakers on the dias in a row so that all the three speakers

a, b, c

do not sit together is

HARD

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

, then

MEDIUM

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

In a group of

6

boys and

4

girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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)

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

HARD

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

A five-digit number divisible by

3

is to be formed using the numerals

0, 1, 2, 3, 4

and

5

without repetition. The total number of ways this can be done is

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

The number of diagonals of a polygon with

15

sides is

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

{}^{n}P_{4} = 20^{n} P_{2}

where

P

denotes the number of permutations, then

n =

________

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

A password is set with

3

distinct letters from the word LOGARITHMS. How many such passwords can be formed?

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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?

HARD

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

Sum of last

30

coefficents in the binomial expansion of

{(1 + x)}^{59}

HARD

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

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Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

,

then

r

is equal to

MEDIUM

Quantitative Aptitude>Arithmetic>Counting Principles>Permutation

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

There are 15 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 15 points.

Important Questions on Counting Principles

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There are $15$ points in a plane out of which $6$ are collinear. Find the number of lines that can be formed from $15$ points.