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
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?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
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?
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?
If nC12 = nC5, find the value of n.
Find the number of diagonals of (ii) a polygon of 16 sides.
How many triangles can be obtained by joining 12 points, five of which are collinear?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
If mC1 = nC2 , then
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
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 ______.
