हिंदी

Evaluate the Following:14c3

Advertisements
Advertisements

प्रश्न

Evaluate the following:

14C3

Advertisements

उत्तर

We have,

\[{}^{14} C_3 = \frac{14}{3} \times \frac{13}{2} \times \frac{12}{1} \times^{11} C_0\]  [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]
\[\Rightarrow\]\[{}^{14} C_3 = 364\]  [∵ \[{}^n C_0 = 1\]]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.1 [पृष्ठ ८]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.1 | Q 1.1 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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.


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


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?


The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?


Compute:

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

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?


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?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?


Evaluate the following:

12C10


If 15Cr : 15Cr − 1 = 11 : 5, find r.


If 16Cr = 16Cr + 2, find rC4.


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


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.


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


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?


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?


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


If nC12 = nC8 , then n =


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 value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is


Find the value of 15C4 


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?


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 one boy and one girl


If nC12 = nC8, then n is equal to ______.


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 ______.


A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.


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 ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C25C2.


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 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

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 ______.


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


There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.


A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×