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
Prove that: n! (n + 2) = n! + (n + 1)!
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
If P (n, 5) = 20. P(n, 3), find n ?
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
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.
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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 vowels are always together?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
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 permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with O and ends with L?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
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 4 letters are used at a time?
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE
Find the number of words formed by permuting all the letters of the following words:
INDIA
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?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
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?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all 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?
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
