Advertisements
Advertisements
प्रश्न
Evaluate the following:
Advertisements
उत्तर
We have,
[∵\[{}^n C_r = {}^n C_{n - r}\]]
[∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]
APPEARS IN
संबंधित प्रश्न
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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?
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?
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?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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 three-digit numbers are there with no digit repeated?
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?
Evaluate the following:
12C10
Evaluate the following:
35C35
If 28C2r : 24C2r − 4 = 225 : 11, 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?
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?
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?
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 (i) no girl?
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 an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
If nCr + nCr + 1 = n + 1Cx , then x =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
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
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
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.
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
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.
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
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 ______.
A convex polygon has 44 diagonals. Find the number of its sides.
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?
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 12C2 – 5C2.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
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 ______.
