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
If nC8 = nC2, find nC2.
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
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:
(i)\[\frac{30!}{28!}\]
Compute:
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
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.
Evaluate the following:
If nC4 = nC6, find 12Cn.
If nC10 = nC12, find 23Cn.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
Find the number of diagonals of , 1.a hexagon
Find the number of diagonals of (ii) a polygon of 16 sides.
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?
Find the number of (i) diagonals
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr = 20Cr + 4 , then rC3 is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If mC1 = nC2 , then
If nC12 = nC8 , then n =
If nCr + nCr + 1 = n + 1Cx , then x =
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
The number of diagonals that can be drawn by joining the vertices of an octagon is
Find the value of 80C2
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
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
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 ______.
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 (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 ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
