Consider all possible permutations of the let | vedclass

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

Question

(B) The word $EARTHQUAKE$ consists of $10$ letters: $E, A, R, T, H, Q, U, A, K, E$.The frequency of letters is: $E: 2, A: 2, R: 1, T: 1, H: 1, Q: 1, U

Vedclass · Accepted Answer

$\frac{7!}{2!}$

Vedclass · Answer

(B) The word $EARTHQUAKE$ consists of $10$ letters: $E, A, R, T, H, Q, U, A, K, E$.The frequency of letters is: $E: 2, A: 2, R: 1, T: 1, H: 1, Q: 1, U: 1, K: 1$.To find the number of permutations containing the word $RAHU$,we treat the block $(RAHU)$ as a single unit.Now,the remaining letters are $E, E, A, T, Q, K$.Including the block $(RAHU)$,we have a total of $7$ items to arrange: $(RAHU), E, E, A, T, Q, K$.Among these $7$ items,the letter $E$ repeats $2$ times.The number of arrangements is given by the formula $\frac{n!}{p!}$,where $n=7$ and $p=2$ (for the two $E$'s).Thus,the number of permutations is $\frac{7!}{2!} = \frac{5040}{2} = 2520$.

Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

Similar Questions

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

If $a_n = \sum_{r = 0}^n \frac{1}{^nC_r}$,then $\sum_{r = 0}^n \frac{r}{^nC_r}$ equals

In how many ways can a committee consisting of $5$ men and $6$ women be formed from $8$ men and $10$ women?

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module