मराठी

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.1 [पृष्ठ ८]

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If nC8 = nC2, find nC2.


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?


It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


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?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


If 18Cx = 18Cx + 2, find x.


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


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?


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.


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 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?


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


In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons 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?


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?


How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?


Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.


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?


There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.


If C (n, 12) = C (n, 8), then C (22, 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


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


The number of diagonals that can be drawn by joining the vertices of an octagon is


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


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


Find n if `""^6"P"_2 = "n" ""^6"C"_2`


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.


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.


Find the value of 15C4 


Find the value of 20C1619C16 


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


In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?


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 ______.


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

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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×