Advertisements
Advertisements
Question
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
Advertisements
Solution
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is 18.
Explanation:
Let the number of participating teams be n
Given that every two teams played one match with each other.
∴ Total number of matches played = nC2
So nC2 = 153
⇒ `(n(n - 1))/2` = 153
⇒ n2 – n = 306
⇒ n2 – n – 306 = 0
⇒ n2 – 18n + 17n – 306 = 0
⇒ n(n – 18) + 17(n – 18) = 0
⇒ (n – 18)(n + 17) = 0
⇒ n – 18 = 0 and n + 17 = 0
⇒ n = 18, n ≠ – 17
Hence, the value of the filler is 18.
APPEARS IN
RELATED QUESTIONS
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.
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
12C10
Evaluate the following:
35C35
If 18Cx = 18Cx + 2, find x.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
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?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
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?
Find the number of (i) diagonals
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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.
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?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
If 15C3r = 15Cr + 3 , then r is equal to
If mC1 = nC2 , then
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 20C16 – 19C16
How many committee of five persons with a chairperson can be selected from 12 persons.
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
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 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
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 ______.
