Advertisements
Advertisements
प्रश्न
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 ______.
उत्तर
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
संबंधित प्रश्न
Compute:
L.C.M. (6!, 7!, 8!)
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
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,
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?
If 18Cx = 18Cx + 2, find x.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If 2nC3 : nC2 = 44 : 3, find n.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?
Find the number of diagonals of , 1.a hexagon
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.
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 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?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
If 20Cr = 20Cr−10, then 18Cr is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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 must all be of the same colour.
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 ______.
