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.
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 r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
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 n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`
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?
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
Find the number of triangles formed by joining 12 points if four points are collinear
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
15Cr and 11Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the 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.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
