Advertisements
Advertisements
Question
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
Advertisements
Solution
The word PERMUTATIONS has a total 12 letters, in which T – 2, rest all are different.
The positions of P and S have been fixed.
Hence, in this case, required number of arrangements
= `(10!)/(2!)` = 1814400.
APPEARS IN
RELATED QUESTIONS
Evaluate 4! – 3!
if `1/(6!) + 1/(7!) = x/(8!)`, find x
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?
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?
Find r if `""^5P_r = 2^6 P_(r-1)`
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 there are always 4 letters between P and S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
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?
In how many ways can 4 letters be posted in 5 letter boxes?
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 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 that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
The product of r consecutive positive integers is divisible by
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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
The number of ways to arrange the letters of the word “CHEESE”:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four 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?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
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
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
