How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Solution and Explanation
In the word EQUATION, there are 5 vowels, namely, A, E, I, O, and U, and 3 consonants, namely, Q, T, and N.
Since all the vowels and consonants have to occur together, both (AEIOU) and (QTN) can be assumed as single objects.
Then, the permutations of these 2 objects taken all at a time are counted. This number would be \(^2P_2=2!\)
Corresponding to each of these permutations, there are 5! permutations of the five vowels taken all at a time and 3! permutations of the 3 consonants taken all at a time.
Hence, by multiplication principle, required number of words = \(2! \times 5! \times 3! = 1440\)
Top Questions on permutations and combinations
- The number of ways 16 oranges distributed to 4 children, each gets at least one.
- JEE Main - 2026
- Mathematics
- permutations and combinations
The number of strictly increasing functions \(f\) from the set \(\{1, 2, 3, 4, 5, 6\}\) to the set \(\{1, 2, 3, ...., 9\}\) such that \(f(i)>i\) for \(1 \le i \le 6\), is equal to:
- JEE Main - 2026
- Mathematics
- permutations and combinations
- If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is
- JEE Main - 2026
- Mathematics
- permutations and combinations
- Let A = \{-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if \(2x + y \le 2\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \(l + m + n\) is equal to :}
- JEE Main - 2026
- Mathematics
- permutations and combinations
- Let \( S=\{1,2,3,4,5,6,7,8,9\} \). Let \( x \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only one digit is repeated and it is repeated exactly twice. Let \( y \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only two digits are repeated and each of these is repeated exactly twice. Then:
- JEE Main - 2026
- Mathematics
- permutations and combinations
Questions Asked in CBSE Class XI exam
- Write the resonance structures for SO3 , NO2 and NO3-
- CBSE Class XI
- Kossel-Lewis Approach to Chemical Bonding
- The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10–19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: FeSO4, MnCl2, ZnCl2 and CdCl2. in which of these solutions precipitation will take place?
- CBSE Class XI
- Law Of Chemical Equilibrium And Equilibrium Constant
- The story is divided into pre-War and post-War times. What hardships do you think the girl underwent during these times?
- CBSE Class XI
- The address
- Have you known someone like the author’s grandmother? Do you feel the same sense of loss with regard to someone whom you have loved and lost?
- CBSE Class XI
- The Portrait of a lady
- In the alkane \( H_3C-CH_2-C(CH_3)_2-CH_2-CH(CH_3)_2\) , identify 1°,2°,3° carbon atoms and give the number of H atoms bonded to each one of these.
- CBSE Class XI
- Alkanes
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.