Advertisements
Advertisements
प्रश्न
Evaluate the following:
n + 1Cn
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 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.
Compute:
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?
In how many ways can an examinee answer a set of ten true/false type questions?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
In how many ways can six persons be seated in a row?
How many 9-digit numbers of different digits can be formed?
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?
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If α = mC2, then find the value of αC2.
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 tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
If 15C3r = 15Cr + 3 , then r is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
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?
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
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 include 2 particular players?
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
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 ______.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
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 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
C1 | C2 |
(a) One book of each subject; | (i) 3968 |
(b) At least one book of each subject: | (ii) 60 |
(c) At least one book of English: | (iii) 3255 |
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.