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
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Find x in each of the following:
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 numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n 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.
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters 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
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
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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
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?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
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?
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 divisible by 4?
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?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
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 different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
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 ______.
