Advertisements
Advertisements
प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
उत्तर
`(""^(2n)C_3)/(""^nC_3) = 11/1`
⇒ `((2n)!)/(3!(2n - 3)!) xx (3!(n - 3)!)/(n!) = 11/1`
⇒ `((2n)(2n - 1)(2n - 2)(2n - 3)!)/((2n - 3)!) xx ((n - 3)!)/(n(n - 1)(n - 2)(n - 3)!) = 11`
⇒ `(2(2n - 1)(2n - 2))/((n - 1)(n - 2)) = 11`
⇒ `(4(2n - 1)(n - 1))/((n - 1)(n - 2)) = 11`
⇒ `(4(2n - 1))/((n - 2)) = 11`
⇒ 4(2n - 1) = 11(n - 2)
⇒ 8n - 4 = 11n - 22
⇒ 11n - 8n = -4 + 22
⇒ 3n = 18
⇒ n = 6
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
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, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
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?
Compute:
L.C.M. (6!, 7!, 8!)
Prove that
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
Evaluate the following:
12C10
If 2nC3 : nC2 = 44 : 3, find n.
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?
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
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?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr = 20Cr−10, then 18Cr is equal to
If 20Cr = 20Cr + 4 , then rC3 is equal to
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If nC12 = nC8 , then n =
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
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
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
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.
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 they can be of any colour
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
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?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
