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
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
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
How many chords can be drawn through 21 points on a circle?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
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 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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
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?
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 odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
If nC12 = nC5, find the value of n.
If 8Cr − 7C3 = 7C2, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Find the number of ways in which : (a) a selection
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
Find the value of 15C4
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
If nC12 = nC8, then n is equal to ______.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
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 ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
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?
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
