Advertisements
Advertisements
प्रश्न
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Advertisements
उत्तर
Let there be n participants present in the meeting.
A handshake occurs between 2 persons.
Then, the number of ways of selecting any 2 persons from them = nC2
Now, in all 66 handshakes were exchanged.
∴ nC2 = 66
∴ `("n"!)/(("n" - 2)!2!)` = 66
∴ `("n" xx ("n" - 1) xx ("n" - 2)!)/(("n" - 2)!)` = 66 × 2
∴ n(n – 1) = 132
∴ n(n – 1) = 12 × 11
Comparing on both sides, we get
∴ n = 12
∴ The number of participants in the meeting = 12
APPEARS IN
संबंधित प्रश्न
Find the value of `""^80"C"_2`
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find the number of triangles formed by joining 12 points if no three points are collinear,
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?
Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Find r if 14C2r : 10C2r–4 = 143 : 10
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn
Find the number of triangles formed by joining 12 points if four points are collinear
Find n if nC8 = nC12
Find n if 23C3n = 23C2n+3
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Answer the following:
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections
Answer the following:
30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.
Answer the following:
There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team
