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
If nC8 = nC2, find nC2.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
How many three-digit numbers are there with no digit repeated?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
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`
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
If 8Cr − 7C3 = 7C2, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
Find the number of diagonals of , 1.a hexagon
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Find the number of (ii) triangles
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
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?
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
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
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 20Cr = 20Cr + 4 , then rC3 is equal to
If nC12 = nC8 , then n =
If nCr + nCr + 1 = n + 1Cx , then x =
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
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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 at least one boy and one girl
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 at least three girls.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
