Advertisements
Advertisements
Question
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate 8!
Compute `(8!)/(6! xx 2!)`
How many 4-digit numbers are there with no digit repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, 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?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
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 ?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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 ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
If nP4 = 12(nP2), find n.
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
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 vowels are never together
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?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
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 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
