Advertisements
Advertisements
प्रश्न
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
पर्याय
45
40
39
38
Advertisements
उत्तर
40
Number of straight lines formed by joining the 10 points if we take 2 points at a time =\[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\]
Number of straight lines formed by joining the 4 points if we take 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\]\
But, 4 collinear points, when joined in pairs, give only one line.
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
Prove that
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?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
Evaluate the following:
35C35
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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(iii) at least 3 girls?
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: atmost 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 15C3r = 15Cr + 3 , then r is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the value of 80C2
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
If α = mC2, then αC2 is equal to.
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
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?
If nC12 = nC8, then n is equal to ______.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
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 ______.
