मराठी

If 15cr : 15cr − 1 = 11 : 5, Find R.

Advertisements
Advertisements

प्रश्न

If 15Cr : 15Cr − 1 = 11 : 5, find r.

Advertisements

उत्तर

Given:
 15Cr : 15Cr − 1 = 11 : 5
We have,

\[\frac{{}^{15} C_r}{{}^{15} C_{r - 1}} = \frac{11}{5}\]

\[\Rightarrow \frac{15 - r + 1}{r} = \frac{11}{5}\]
\[\frac{{}^n C_r}{{}^n C_{r - 1}} = \frac{n - r + 1}{r}\]

\[\Rightarrow 75 - 5r + 5 = 11r\]
\[ \Rightarrow 16r = 80\]
\[ \Rightarrow r = 5\]

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

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.1 | Q 9 | पृष्ठ ८

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


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?


Compute:

\[\frac{11! - 10!}{9!}\]

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


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?


How many three-digit numbers are there with no digit repeated?


How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?


How many 9-digit numbers of different digits can be formed?


Evaluate the following:

\[\sum^5_{r = 1} {}^5 C_r\]

 


24Cx = 24C2x + 3, find x.


If 8Cr − 7C3 = 7C2, find r.


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


There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:

a particular student is included.


How many different selections of 4 books can be made from 10 different books, if
there is no restriction;


How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;


From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least 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 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?


Find the number of (i) diagonals


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: exactly 3 girls?


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: atmost 3 girls?


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 = 20Cr + 4 , then rC3 is equal to


If 15C3r = 15Cr + 3 , then r is equal to


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


If n + 1C3 = 2 · nC2 , then n =


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.


Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.


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 they must all be of the same colour.


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.


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 ______.


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 ______.


A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.


Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×