Advertisements
Advertisements
प्रश्न
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
पर्याय
11
12
13
14
Advertisements
उत्तर
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is 12.
Explanation:
Let the total number of persons in a room be n since, two persons make 1 handshake
∴ The number of handshakes = nC2
So nC2 = 66
⇒ `(n!)/(2!(n - 2)!)` = 66
⇒ `(n(n - 1)(n - 2)!)/(2 xx 1 xx (n - 2)1)` = 66
⇒ `(n(n - 1))/2` = 66
⇒ n2 – n = 132
⇒ n2 – n – 132 = 0
⇒ n2 – 12n + 11n – 132 = 0
⇒ n(n – 12) + 11(n – 12) = 0
⇒ (n – 12)(n + 11) = 0
⇒ n – 12 = 0, n + 11 = 0
⇒ n = 12, n = – 11
∴ n = 12 ....(∵ n ≠ – 11)
APPEARS IN
संबंधित प्रश्न
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
Twelve students complete in a race. In how many ways first three prizes be given?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
Evaluate the following:
14C3
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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?
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
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
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
If 20Cr + 1 = 20Cr − 1 , then r is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow 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.
There are 8 doctors and 4 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.
Find the value of 15C4
Find the value of 80C2
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
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 two must be white and two red
If nC12 = nC8, then n is equal to ______.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
