Advertisements
Advertisements
प्रश्न
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Advertisements
उत्तर
Given `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10
nPr =`("n"!)/(("n" - "r")!)`
`(("n" - 1)"P"_3)/(""^"n""P"_4) = 1/10`
`((("n" - 1)!)/(("n" - 1 - 3)!))/(("n"!)/(("n" - 4)!)) = 1/10`
`(("n" - 1)!)/(("n" - 4)!) xx (("n" - 4)!)/("n"!) = 1/10`
`(("n" - 1)!)/("n"!) = 1/10`
`(("n" - 1)!)/("n"("n" - 1)!)= 1/10`
`1/"n" = 1/10`
⇒ n = 10
APPEARS IN
संबंधित प्रश्न
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
