Advertisements
Advertisements
प्रश्न
If n + 1C3 = 2 · nC2 , then n =
विकल्प
3
4
5
6
Advertisements
उत्तर
5
\[\ ^{n + 1}{}{C}_3 = 2 \times \ ^{n}{}{C}_2 \]
\[ \Rightarrow \frac{\left( n + 1 \right)!}{3! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n + 1 \right) n!}{3 \times 2! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow n + 1 = 6\]
\[ \Rightarrow n = 5\]
APPEARS IN
संबंधित प्रश्न
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?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
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?
Compute:
Prove that
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?
How many three-digit odd numbers are there?
Evaluate the following:
12C10
Evaluate the following:
n + 1Cn
If nC10 = nC12, find 23Cn.
If 18Cx = 18Cx + 2, find x.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
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?
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?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
5C1 + 5C2 + 5C3 + 5C4 +5C5 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
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
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
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
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.
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Find the value of 15C4
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?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
If nC12 = nC8, then n is equal to ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
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 |
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 |
