English

Find the value of 80C2

Advertisements
Advertisements

Question

Find the value of 80C2

Sum
Advertisements

Solution

80C2 = `(80!)/(2!(80 - 2)!)`

= `(80!)/(2! 78!)`

= `(80 xx 79 xx 78!)/(2 xx 78!)`

= 40 × 79

= 3160

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Permutations and Combination - Exercise 3.6 [Page 64]

APPEARS IN

RELATED QUESTIONS

Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


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?


How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?


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: 

(i)\[\frac{30!}{28!}\]


There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?


How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


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?


Evaluate the following:

14C3


Evaluate the following:

n + 1Cn


If nC12 = nC5, find the value of n.


If 15C3r = 15Cr + 3, find r.


If 15Cr : 15Cr − 1 = 11 : 5, find r.


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

include 2 particular players?


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.


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?


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


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


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?


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


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 no girls


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


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.


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 ______.


The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them 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 ______.


If some or all of n objects are taken at a time, the number of combinations is 2n – 1.


The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.


There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, 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 ______.


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×