मराठी

There Are 10 Points in a Plane of Which 4 Are Collinear. How Many Different Straight Lines Can Be Drawn by Joining These Points.

Advertisements
Advertisements

प्रश्न

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

Advertisements

उत्तर

Number of straight lines formed joining the 10 points, taking 2 points at a time = 

\[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\]
Number of straight lines formed joining the 4 points, taking 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\]
But, when 4 collinear points are joined pair wise, they give only one line.
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.2 [पृष्ठ १६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.2 | Q 14 | पृष्ठ १६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


Compute: 

(i)\[\frac{30!}{28!}\]


Compute:

 L.C.M. (6!, 7!, 8!)


A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?


A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?


There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?


In how many ways can an examinee answer a set of ten true/false type questions?


How many three-digit numbers are there with no digit repeated?


In how many ways can six persons be seated in a row?


How many 9-digit numbers of different digits can be formed?


Evaluate the following:

n + 1Cn


If nC4 = nC6, find 12Cn.


f 24Cx = 24C2x + 3, find x.


If 15Cr : 15Cr − 1 = 11 : 5, find r.


If nC4 , nC5 and nC6 are in A.P., then find n.


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

 exclude 2 particular players?


There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


How many triangles can be obtained by joining 12 points, five of which are collinear?


In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl? 


Find the number of (i) diagonals


Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?


Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is


Find the value of 80C2


In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?


If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?


A convex polygon has 44 diagonals. Find the number of its sides.


In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?


In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?


A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


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 arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×