English

If C (N, 12) = C (N, 8), Then C (22, N) is Equal to (A) 231 (B) 210 (C) 252 (D) 303

Advertisements
Advertisements

Question

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

Options

  • 231

  • 210

  •  252

  • 303

MCQ
Advertisements

Solution

231

\[{}^n C_{12} =^n C_8\]
\[\Rightarrow n = 12 + 8 = 20\] [∵ \[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]
Now,
\[{}^{22} C_n =^{22} C_{20}\]
\[= \frac{22}{2} \times \frac{21}{1}\]
\[= 231\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.5 [Page 25]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.5 | Q 5 | Page 25

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.


Compute:

 L.C.M. (6!, 7!, 8!)


A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?


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


Evaluate the following:

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

 


In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?


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


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


Find the number of diagonals of (ii) a polygon of 16 sides.


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 there is exactly one ace in each combination.


If mC1 nC2 , then


In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?


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 C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


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


Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?


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


Find the value of 15C4 


If α = mC2, then αCis equal to.


In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?


How many committee of five persons with a chairperson can be selected from 12 persons.


If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.


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 can be of any colour


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?


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


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 ______.


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. He can choose the seven questions in 650 ways.


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

The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.


There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.


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×