Problem Solving

How many different words can be made from the word REVIEW, such that W is always before R?

(Sorry I don't have options)

a total of 6!=6*5*4*3*2*1=720 different words can be made from these six letters
the possibilty that W is before R and R is before W is the same
thus we have 720*50%=360

seanceserene wrote:a total of 6!=6*5*4*3*2*1=720 different words can be made from these six letters
the possibilty that W is before R and R is before W is the same
thus we have 720*50%=360

Good call that we can simply divide the total by two since the number with R before W and vice versa would be the same. However, we also need to account for the fact that the word has two Es. Therefore, you need to take 6!/2! in the overall total. Final answer should be 180.

Note: E.g. If you take 6! instead of 6!/2! you are counting EERVIW twice

arzanr wrote:

seanceserene wrote:a total of 6!=6*5*4*3*2*1=720 different words can be made from these six letters
the possibilty that W is before R and R is before W is the same
thus we have 720*50%=360

Good call that we can simply divide the total by two since the number with R before W and vice versa would be the same. However, we also need to account for the fact that the word has two Es. Therefore, you need to take 6!/2! in the overall total. Final answer should be 180.

Note: E.g. If you take 6! instead of 6!/2! you are counting EERVIW twice

Great! thank you for pointing out my mistake!!
carelessness is my greatest enemy in Math
hope that i don't make the same mistake next time

the word REVIEW can be grouped in 6! ways=6*5*4*3*2*1= 720
since two E present in the word, divide eq 720 by 2!=> 360
since W is always before R divide 360 by 2!=180