Advertisements
Advertisements
प्रश्न
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Advertisements
उत्तर
∴ `(""^(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
संबंधित प्रश्न
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
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 different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
If nC4 , nC5 and nC6 are in A.P., then find n.
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
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(iii) at least 3 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
If mC1 = nC2 , then
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 from the lot.
A convex polygon has 44 diagonals. Find the number of its sides.
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
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
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 ______.
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 (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 ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
