The number of 4 letter words (with or without | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The word $'EXAMINATION'$ contains $11$ letters: $A, A, I, I, N, N, E, X, M, T, O$. There are $8$ distinct letters: ${A, I, N, E, X, M, T, O}$. The

Vedclass · Accepted Answer

$2454$

Vedclass · Answer

(D) The word $'EXAMINATION'$ contains $11$ letters: $A, A, I, I, N, N, E, X, M, T, O$. There are $8$ distinct letters: ${A, I, N, E, X, M, T, O}$. The frequency of letters is: $A: 2, I: 2, N: 2, E: 1, X: 1, M: 1, T: 1, O: 1$. We need to form $4$ letter words. The cases are:$1$. Two letters of one kind and two letters of another kind:Selection: $^3C_2 = 3$ ways. Arrangement: $3 	imes \frac{4!}{2!2!} = 3 	imes 6 = 18$ ways.$2$. Two letters of one kind and two different letters:Selection: $^3C_1$ (for the pair) $	imes ^7C_2$ (for the two different letters) $= 3 	imes 21 = 63$ ways. Arrangement: $63 	imes \frac{4!}{2!} = 63 	imes 12 = 756$ ways.$3$. All four letters are different:Selection: $^8C_4 = 70$ ways. Arrangement: $70 	imes 4! = 70 	imes 24 = 1680$ ways.Total number of words $= 18 + 756 + 1680 = 2454$.

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

Similar Questions

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is:

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

$A$ code word is to consist of $2$ English alphabets followed by $2$ distinct numbers between $1$ and $9$. For example,$CA23$ is a code word. How many such code words are there?

In an election,there are $5$ candidates and $3$ vacancies. $A$ voter can vote for a maximum of $3$ candidates. In how many ways can a voter cast their vote?

Vedclass Test Series

Exam Paper Generator

Online Exam Module