The letters of the word ASSASSIN are written | vedclass

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

Question

(B) The word $ASSASSIN$ contains $8$ letters: $A(2), S(4), I(1), N(1)$.Total number of arrangements $ = \frac{8!}{4! 	imes 2!} = \frac{8 	imes 7 	i

Vedclass · Accepted Answer

$\frac{1}{14}$

Vedclass · Answer

(B) The word $ASSASSIN$ contains $8$ letters: $A(2), S(4), I(1), N(1)$.Total number of arrangements $ = \frac{8!}{4! 	imes 2!} = \frac{8 	imes 7 	imes 6 	imes 5 	imes 4!}{4! 	imes 2} = 840$.To ensure no two $S$ occur together,we use the gap method. First,arrange the remaining $4$ letters $(A, A, I, N)$.The number of ways to arrange these $4$ letters is $\frac{4!}{2!} = 12$.These $4$ letters create $5$ gaps (including ends): $\_ L_1 \_ L_2 \_ L_3 \_ L_4 \_$.We need to place $4$ $S$'s in these $5$ gaps. The number of ways to choose $4$ gaps out of $5$ is $\binom{5}{4} = 5$.Total favorable arrangements $ = 12 	imes 5 = 60$.Probability $ = \frac{	ext{Favorable arrangements}}{	ext{Total arrangements}} = \frac{60}{840} = \frac{1}{14}$.

The letters of the word $ASSASSIN$ are written down at random in a row. The probability that no two $S$ occur together is

Similar Questions

Tickets numbered $1$ to $20$ are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of $3$ or $5$?

$A$ person draws a card from a pack of playing cards,replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in the first two attempts is

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball taken out is red,what is the probability that the second ball taken out is also red?

From $10,000$ lottery tickets numbered from $1$ to $10,000$,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?

The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module