2 questions (help me out)?

Question

Q1) Ten students are placed at random in a line. What is the probability that the two oldest students are separated?

The answer is 0.8...

But I don't understand...

Q2) In how many ways can the letters of the word FACETIOUS be arranged in a line? What is the probability that an arrangement begins with F and ends with S.

The first part I know how to do.

Answer is 9!

But I'm unsure of the second part (the part on the probability thingy).

Please help me out,

Explanations are greatly appreciated.

Thank you!

(:

Answer 1

Q2) the probability that it begins with F is 1/9 and the probability that last letter is S is 1/8, so the probability of both happening at the same time should be 1/9*1/8= 1/72

(sorry, messed it up the first time, like I said - it's been a long time since high school...)

Answer 2

Not 9 for Q2.  It's 9!, which is 9x8x7x6x5x4x3x2, which is 362880.

For Q2 part 2, you now know the first and second letters.  There is only one possible value for them, so lets fill those in.

1x_x_x_x_x_x_x_x1

The other 7 can be in any order, so we put 7! in there like this.

1x7x6x5x4x3x2x1x1

That's 5040.  The probability is 5040/362880, which is 1/72.

Answer 3

there are only 10 people it would be hard for them to be next to each other and just take them out and you have 80% left

i think it is 1:81 since there are 9 numbers and you would just square the letters

Answer 4

In ques 1 the answer is 0.8