Advertisements
Advertisements
Question
Find n if n – 1P3 : nP4 = 1 : 9
Advertisements
Solution
n – 1P3 : nP4 = 1 : 9
`=> (""^("n" - 1)"P"_3)/(""^"n""P"_4) = 1/9`
⇒ `[ ((n - 1)!)/((n - 1 - 3)!)]/[(n!)/((n - 4)!)] = 1/9`
⇒ `((n - 1)!)/((n - 4)!) xx ((n - 4)!)/(n!) = 1/9`
⇒ `((n - 1)!)/(n xx (n - 1)!) = 1/9`
⇒ `1/n = 1/9`
∴ n = 9
APPEARS IN
RELATED QUESTIONS
Evaluate 8!
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
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?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
The number of five-digit telephone numbers having at least one of their digits repeated is
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
The number of ways to arrange the letters of the word CHEESE are
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The possible outcomes when a coin is tossed five times:
The number of ways to arrange the letters of the word “CHEESE”:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The total number of 9 digit numbers which have all different digits is ______.
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 different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
