Advertisements
Advertisements
प्रश्न
Find n if n – 1P3 : nP4 = 1 : 9
Advertisements
उत्तर
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
संबंधित प्रश्न
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
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 natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`(3! + 1!)/(2^2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
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
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
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.
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?
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The total number of 9 digit numbers which have all different digits is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
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 ______.
