How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Solution and Explanation
There are 8 different letters in the word EQUATION.
Therefore, the number of words that can be formed using all the letters of the word EQUATION, using each letter exactly once, is the number of permutations of 8 different objects taken 8 at a time, which is \(^8P_8=8!\)
Thus, required number of words that can be formed =\( 8! = 40320\)
Top Questions on Permutations
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Mathematics
- Permutations
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
- BITSAT - 2025
- Mathematics
- Permutations
- From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.
- AP EAPCET - 2025
- Mathematics
- Permutations
- 5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $
- AP EAPCET - 2025
- Mathematics
- Permutations
- The number of positive integers less than 10000 which contain the digit 5 at least once is
- AP EAPCET - 2025
- Mathematics
- Permutations
Questions Asked in CBSE Class XI exam
(i) List the deeds that led Ray Johnson to describe Akhenaten as “wacky”.
(ii) What were the results of the CT scan?
(iii) List the advances in technology that have improved forensic analysis.
(iv) Explain the statement, “King Tut is one of the first mummies to be scanned — in death, as in life...”- CBSE Class XI
- Discovering Tut: The saga Continues
- 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
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
- Write a note on economic importance of algae and gymnosperms.
- CBSE Class XI
- Bryophytes
- Briefly comment on "The author’s meeting with Norbu."
- CBSE Class XI
- Silk road
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.