English

F 24cx = 24c2x + 3, Find X. - Mathematics

Advertisements
Advertisements

Question

24Cx = 24C2x + 3, find x.

Advertisements

Solution

Given:
 24Cx = 24C2x + 3
We have,

\[24 = x + 2x + 3\] [∵\[{}^n C_x = {}^n C_y \Rightarrow x = y\]]  or, \[n = x + y\]
\[\Rightarrow 24 = 3x + 3\]
\[ \Rightarrow 3x = 21\]
\[ \Rightarrow x = 7\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.1 [Page 8]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.1 | Q 5 | Page 8

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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.


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?


If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


Compute:

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

Compute:

 L.C.M. (6!, 7!, 8!)


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


In how many ways can an examinee answer a set of ten true/false type questions?


A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?


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 different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?


Evaluate the following:

14C3


If nC12 = nC5, find the value of n.


How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?


Find the number of diagonals of , 1.a hexagon


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?


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 ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


If 20Cr = 20Cr−10, then 18Cr is equal to


If 20Cr = 20Cr + 4 , then rC3 is equal to


If mC1 nC2 , then


If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =


5C1 + 5C2 5C3 + 5C4 +5C5 is equal to


There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is


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


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


Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120


Find the value of 15C4 + 15C5 


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.


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 ______.


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 ______.


Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red 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 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 ______.


There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.


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×