The number of four-letter words that can be f | vedclass

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

Question

(B) To form a four-letter word using the letters $a, b, c$ such that all three letters occur,we must select one letter to be repeated twice and the ot

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) To form a four-letter word using the letters $a, b, c$ such that all three letters occur,we must select one letter to be repeated twice and the other two letters to appear once each.Step $1$: Select the letter to be repeated from the set $\{a, b, c\}$. This can be done in $^3C_1 = 3$ ways.Step $2$: Arrange the four letters (e.g.,if $a$ is repeated,the letters are $a, a, b, c$). The number of ways to arrange these four letters is $\frac{4!}{2!} = \frac{24}{2} = 12$.Step $3$: The total number of words is the product of the number of ways to select the letter and the number of ways to arrange them:$3 	imes 12 = 36$.

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

Similar Questions

Find the number of $4$ letter words,with or without meaning,which can be formed out of the letters of the word $ROSE$,where the repetition of the letters is not allowed.

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the members of the same family are not separated?

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $SACHIN$?

In how many ways can the letters of the word $TRIANGLE$ be arranged such that no two vowels occur together?

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module