In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Solution and Explanation
In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once.
Since all the words have to be arranged in such a way that all the Ss are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for 10 objects.
These 10 objects in which there are 3 As, 2 Is, and 2 Ns can be arranged in \(\frac{10!}{3!2!2!}\) ways.
Thus, required number of ways of arranging the letters of the given word
\(=\frac{10!}{3!2!2!}=151200\)
Top Questions on permutations and combinations
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- BITSAT - 2025
- Mathematics
- permutations and combinations
- If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to
- JEE Main - 2025
- Mathematics
- permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
Match List-I with List-II
List-I List-II (A) \(^{8}P_{3} - ^{10}C_{3}\) (I) 6 (B) \(^{8}P_{5}\) (II) 21 (C) \(^{n}P_{4} = 360,\) then find \(n\). (III) 216 (D) \(^{n}C_{2} = 210,\) find \(n\). (IV) 6720
Choose the correct answer from the options given below:- CUET (UG) - 2025
- General Aptitude
- permutations and combinations
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
Questions Asked in CBSE Class XI exam
- Solve the following inequalities and represent the solution graphically on number line: 3x –7 > 2(x-6), 6-x > 11-2x.
- CBSE Class XI
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- Prove that, cos 6 x = 32cos6 x-48cos4 x+18cos2 x -1.
- CBSE Class XI
- Trigonometric Functions of Sum and Difference of Two Angles
- Three reasons why the author’s grandmother was disturbed when he started going to the city school.
- CBSE Class XI
- The Portrait of a lady
- Prove that cos2 2x-cos2 6x = sin 4x sin 8x
- CBSE Class XI
- Trigonometric Functions of Sum and Difference of Two Angles
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
- Discovering Tut: The saga Continues
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.