Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
उत्तर
There are total 13 letters in ASSASSINATION, in which A is used three times, S four times, I twice and N twice. 4 – S have to live together. Therefore, it was considered a letter. Thus, 10 letters remain in it in which 3 – A, 2 – 1 and 2 – N are the same.
∴ The arrangement of letters of this word when S remains together
= `(10)/(322)`
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/((3 xx 2 xx 1)xx(2 xx 1) xx (2 xx 1))`
= 151200
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
How many 4-digit numbers are there with no digit 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?
Which of the following are true:
(2 +3)! = 2! + 3!
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?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
6P6
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of arrangements of the letters of the word BANANA in which two N's come 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 five-digit telephone numbers having at least one of their digits repeated is
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of ways to arrange the letters of the word CHEESE are
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
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The total number of 9 digit number which has all different digit is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
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?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
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:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
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.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
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 ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
