Advertisements
Advertisements
प्रश्न
If 2nC3 : nC2 = 44 : 3, find n.
Advertisements
उत्तर
Given:
\[ \Rightarrow \frac{2n!}{3! (2n - 3)!} \times \frac{2! (n - 2)!}{n!} = \frac{44}{3}\]
\[ \Rightarrow \frac{2n (2n - 1) (2n - 2)}{3 n (n - 1)} = \frac{44}{3}\]
\[ \Rightarrow (2n - 1) (2n - 2) = 22 (n - 1)\]
\[ \Rightarrow 4 n^2 - 6n + 2 = 22n - 22\]
\[ \Rightarrow 4 n^2 - 28n + 24 = 0\]
\[ \Rightarrow n^2 - 7n + 6 = 0\]
\[ \Rightarrow n^2 - 6n - n + 6 = 0\]
\[ \Rightarrow n (n - 6) - 1(n - 6) = 0\]
\[ \Rightarrow (n - 1) (n - 6) = 0\]
APPEARS IN
संबंधित प्रश्न
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.
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
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?
Compute:
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
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?
If nC12 = nC5, find the value of n.
If 8Cr − 7C3 = 7C2, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
If α = mC2, then find the value of αC2.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
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 professor is included.
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 included.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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 group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
Find the number of (ii) triangles
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?
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?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 20Cr + 1 = 20Cr − 1 , then r is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
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
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw 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 ______.
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 ______.
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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
