Advertisements
Advertisements
Question
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Advertisements
Solution
When n = 9, r = 5 `(n!)/((n-r)!) = (9!)/((9 - 5)!) = (9!)/(4!) = (9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(4!)`
= 9 x 8 x 7 x 6 x 5 = 15120
APPEARS IN
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Which of the following are true:
(2 +3)! = 2! + 3!
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?
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 5 different balls be distributed among three boxes?
Evaluate each of the following:
P(6, 4)
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
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 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
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
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
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
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
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 numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
The possible outcomes when a coin is tossed five times:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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 distinct 6-digit numbers are there?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
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?
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 permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
