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
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Find x in each of the following:
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
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 three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
In how many ways can 7 letters be posted in 4 letter boxes?
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?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of arrangements of the word "DELHI" in which E precedes I 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
Find the rank of the word ‘CHAT’ in the dictionary.
The possible outcomes when a coin is tossed five times:
The total number of 9 digit number which has all different digit is:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
Find the distinct permutations of the letters of the word MISSISSIPPI?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
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
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done 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! |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
