Advertisements
Advertisements
प्रश्न
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
Advertisements
उत्तर
P (n − 1, 3):P (n, 4) = 1:9
\[\Rightarrow \frac{\left( n - 1 \right)!}{(n - 1 - 3)!} \times \frac{(n - 4)!}{(n)!} = \frac{1}{9}\]
\[ \Rightarrow \frac{\left( n - 1 \right)!}{\left( n - 4 \right)!} \times \frac{\left( n - 4 \right)!}{n!} = \frac{1}{9}\]
\[ \Rightarrow \frac{\left( n - 1 \right)!}{n!} = \frac{1}{9}\]
\[ \Rightarrow \frac{\left( n - 1 \right)!}{n\left( n - 1 \right)!} = \frac{1}{9}\]
\[ \Rightarrow \frac{1}{n} = \frac{1}{9}\]
\[ \Rightarrow n = 9\]
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
If (n + 2)! = 60 [(n − 1)!], find n.
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
Prove that:
If P (n, 5) = 20. P(n, 3), find n ?
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the letters P and I respectively occupy first and last place?
How many permutations can be formed by the letters of the word, 'VOWELS', when
there is no restriction on letters?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used at a time.
How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if all letters are used but first is vowel.
Find the number of words formed by permuting all the letters of the following words:
SERIES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many number of four digits can be formed with the digits 1, 3, 3, 0?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?
If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
