Advertisements
Advertisements
प्रश्न
Evaluate the following:
n + 1Cn
Advertisements
उत्तर
n + 1Cn =n + 1C1 [∵\[{}^n C_r = {}^n C_{n - r}\]]
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
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?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
How many three-digit numbers are there?
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.
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
If 2nC3 : nC2 = 44 : 3, find n.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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 excluded.
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
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: at least 3 girls?
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?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
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 20Cr = 20Cr + 4 , then rC3 is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
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
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
If n + 1C3 = 2 · nC2 , then n =
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the value of 80C2
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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.
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?
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
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 ______.

