Advertisements
Advertisements
Question
Evaluate the following:
n + 1Cn
Advertisements
Solution
n + 1Cn =n + 1C1 [∵\[{}^n C_r = {}^n C_{n - r}\]]
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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?
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?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Evaluate the following:
12C10
If 28C2r : 24C2r − 4 = 225 : 11, find r.
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
exclude 2 particular players?
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?
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 (i) diagonals
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 the selection be made?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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.
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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.
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
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Find the value of 15C4
Find the value of 80C2
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 ______.
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
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines 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 ______.
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.
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.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
