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 `(n!)/((n-r)!)`, when n = 9, r = 5
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = ""^6P_(r-1)`
Find x in each of the following:
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?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
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?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
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 ?
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
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 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 letters of the word BHARAT taking 3 at a time 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
Find x if `1/(6!) + 1/(7!) = x/(8!)`
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The possible outcomes when a coin is tossed five times:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The total number of 9 digit number which has all different digit is:
The number of ways to arrange the letters of the word “CHEESE”:
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 student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
8 women and 6 men are standing in a line. In how many arrangements will all 6 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?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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
DANGER
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
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)`
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.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
