Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
Find the value of `""^80"C"_2`
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find n if `""^"n""C"_("n" - 3)` = 84
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find the differences between the largest values in the following: `""^13"C"_r "and" ""^8"C"_r`
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 committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Find n if 2nCr–1 = 2nCr+1
Find n if nCn–2 = 15
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
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:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
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
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
