हिंदी

If 8cr − 7c3 = 7c2, Find R. - Mathematics

Advertisements
Advertisements

प्रश्न

If 8Cr − 7C3 = 7C2, find r.

Advertisements

उत्तर

Given:
 8Cr − 7C3 = 7C2
We have,\[{}^8 C_r = {}^7 C_2 + {}^7 C_3\]

\[\Rightarrow {}^8 C_r =^8 C_3\] [∵\[{}^n C_r + {}^n C_{r - 1} = {}^{n + 1} C_r\]]
\[r \leq n\]
\[\Rightarrow r = 3\] [∵\[{}^n C_x = {}^n C_y \Rightarrow x = y\]]  or,\[n = x + y\]
\[\text{And}r + 3 = 8\]
\[ \Rightarrow r = 5\]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.1 [पृष्ठ ८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.1 | Q 8 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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.


Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.


In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?


A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?


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?


If nC10 = nC12, find 23Cn.


If n +2C8 : n − 2P4 = 57 : 16, find n.


From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?


How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?


From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer


How many triangles can be obtained by joining 12 points, five of which are collinear?


Find the number of (i) diagonals


Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?


Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.


A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.


Find the number of ways in which : (a) a selection


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


If 20Cr + 1 = 20Cr − 1 , then r is equal to


If C (n, 12) = C (n, 8), then C (22, n) is equal to


How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120


If 43Cr − 6 = 43C3r + 1 , then the value of r is


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.


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 20C1619C16 


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.


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 at least three girls.


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 ______.


The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.


15C8 + 15C915C615C7 = ______.


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

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×