Advertisements
Advertisements
प्रश्न
The product of r consecutive positive integers is divisible by
पर्याय
r !
(r − 1) !
(r + 1) !
none of these.
Advertisements
उत्तर
r !
The product of r consecutive integers is equal to r!, so it will be divisible by r!.
APPEARS IN
संबंधित प्रश्न
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
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 ?
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 total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
8P3
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of arrangements of the word "DELHI" in which E precedes I is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, 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
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
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 rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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?
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 ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
