Advertisements
Advertisements
Question
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Advertisements
Solution
∴ `(""^(2"n")"C"_3)/(""^"n""C"_2) = 52/3`
∴ `((2"n")!)/(3!(2"n" - 3)!)÷("n"!)/(2!("n" - 2)!) = 52/3`
∴ `((2"n")!)/(3!(2"n" - 3)!) xx (2!("n" - 2)!)/("n"!) = 52/3`
`∴ ((2"n")(2"n" - 1)(2"n" - 2)(2"n" - 3)!)/(3xx2!(2"n" - 3)!) xx (2!("n" - 2)!)/("n"("n" - 1)("n" - 2)!) = 52/3`
∴ `(2"n"(2"n" - 1) xx 2("n" - 1))/3 xx 1/("n"("n" - 1)) = 52/3`
∴ `(4(2"n" - 1))/3 = 52/3`
∴ 2n – 1 = `52/3 xx 3/4`
∴ 2n – 1 = 13
∴ 2n = 14
∴ n = 7
APPEARS IN
RELATED QUESTIONS
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 coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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 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 15Cr : 15Cr − 1 = 11 : 5, find r.
Find the number of (i) diagonals
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
If 20Cr = 20Cr + 4 , then rC3 is equal to
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
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
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 ______.
