English

Evaluate the Following:12c10

Advertisements
Advertisements

Question

Evaluate the following:

12C10

Advertisements

Solution

We have,

\[{}^{12} C_{10} =^{12} C_2\]         [∵\[{}^n C_r = {}^n C_{n - r}\]]
\[\Rightarrow {}^{12} C_{10} =^{12} C_2 = \frac{12}{2} \times \frac{11}{1} \times^{{}^{10}} C_0\]  [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]
\[\Rightarrow^{12} C_{10} = \frac{12}{2} \times \frac{11}{1} \times 1\]    [∵\[{}^n C_0 = 1\]]
\[\Rightarrow^{12} C_{10} = 66\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.1 [Page 8]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.1 | Q 1.2 | Page 8

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Determine n if  `""^(2n)C_3 : ""^nC_3 = 11: 1`


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


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:

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

Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

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


Evaluate the following:

14C3


Evaluate the following:

n + 1Cn


If nC4 = nC6, find 12Cn.


If nC10 = nC12, find 23Cn.


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


If 16Cr = 16Cr + 2, find rC4.


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 diagonals of , 1.a hexagon


Find the number of (i) diagonals


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.


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?


There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?


Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is


Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.


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.


If α = mC2, then αC2 is equal to.


The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` 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 ______.


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?


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


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 ______.


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 ______.


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 ______.


Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.


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.


A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.


The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?


The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×