Advertisements
Advertisements
Question
Find the value of 80C2
Advertisements
Solution
80C2 = `(80!)/(2!(80 - 2)!)`
= `(80!)/(2! 78!)`
= `(80 xx 79 xx 78!)/(2 xx 78!)`
= 40 × 79
= 3160
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
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?
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?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Evaluate the following:
35C35
If nC10 = nC12, find 23Cn.
If 15C3r = 15Cr + 3, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
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?
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(iii) at least 3 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 20Cr + 1 = 20Cr − 1 , then r is equal to
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 15C4 + 15C5
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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?
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants 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 ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 |
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 ______.
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 ______.

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 ______.
