1) In a survey of 100 students who watch television, 21 watch American Idol, 39 watch Lost, and 8 watch both. How many of the students surveyed watch at least one of the two shows?

2) Consider all the possible arrangements of the letters in the term "ALLSTARS." How many do not have two same letters next to each other?

3) If all multiples of 4 and all multiples of 5 are removed from the set of integers from 1 through 100, how many integers remain?

Thanks!

Rudram592 May 11, 2019

#4**+1 **

1) In a survey of 100 students who watch television, 21 watch American Idol, 39 watch Lost, and 8 watch both. How many of the students surveyed watch at least one of the two shows?

(21 - 8) = 13 = Those that watch "American Idol" only

(39 - 8) = 31 = Those that watch "Lost" only

So....the number that watch at least one is

13 + 8 + 31 =

52

CPhill May 11, 2019

#5**+1 **

3) If all multiples of 4 and all multiples of 5 are removed from the set of integers from 1 through 100, how many integers remain?

We have 25 multiples of 4 and 20 multiples of 5

However....we've "double-counted" the multiples of 4 and 5 = 20, 40, 80 and 100

So

[ 25 + 20 ] - 4 = 41

CPhill May 11, 2019

#6**+1 **

Oops...sorry....you wanted the ones that remain !!!

That would be 100 - 41 = 59

CPhill May 11, 2019