In how many ways can the letters of the word | vedclass

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

Question

(D) The word $ASSASSIN$ contains $9$ letters: $A(2), S(4), I(2), N(1)$.First,arrange the letters other than $S$,which are $A, A, I, I, N$. The number

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The word $ASSASSIN$ contains $9$ letters: $A(2), S(4), I(2), N(1)$.First,arrange the letters other than $S$,which are $A, A, I, I, N$. The number of ways to arrange these $5$ letters is $\frac{5!}{2!2!} = \frac{120}{4} = 30$.These $5$ letters create $6$ gaps (including ends): $\_ A \_ A \_ I \_ I \_ N \_$.We need to place $4$ $S$s in these $6$ gaps so that no two $S$s are together. The number of ways to choose $4$ gaps out of $6$ is $^6C_4 = \frac{6 	imes 5}{2 	imes 1} = 15$.Total number of arrangements = $30 	imes 15 = 450$.

In how many ways can the letters of the word $ASSASSIN$ be arranged so that no two $S$s occur together?

Similar Questions

If $4$-digit numbers greater than $5,000$ are randomly formed from the digits $0, 1, 3, 5,$ and $7$,what is the probability of forming a number divisible by $5$ when the repetition of digits is not allowed?

What is the remainder when $1! + 2! + 3! + \dots + 200!$ is divided by $14$?

$9$ balls are to be placed in $9$ boxes. $3$ boxes are so small that they cannot hold $5$ balls. In how many ways can one ball be placed in each box?

The number of $5$-digit numbers that are not divisible by $5$ and consist of different odd digits is:

All the arrangements,with or without meaning,of the word $FARMER$ are written excluding any word that has two $R$ appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word $FARMER$ in this list is .... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module