Why Can't I Solve These Seemingly Simple Math Problems?

[Frustrated]

simple problems that I can't figure out! HELP!

Hello, first of all, thanks in advance for checking out my thread. below are a short list of some simple problems that should be easy to solve for those of you who frequent this forum. However, I can't seem to figure them out and it is really getting on my nerves. If you have any ideas, i would really appreciate your help. Included with the questions are the numerical answers. As such, I am solely interested in a brief explanation or the steps and formulas required for them. THANKS!

Q) A wire is cut into three equal parts. The resulting segments are then cut into 4,6, and 8 parts respectively. If each of the resulting segments has an integral length, what is the minimum length of the wire?

Q) Oak trees line both sides of a street for a length of (3/8) Km. If there is 16 meters of space between the trees and each tree is 1 meter wide, how many trees are there along the street?

Q) what is the probability of six tails out of nine tosses of a fair coin? (ANS = 21/128)

Q) solve 4 csc2 – 1 = 0 for all values 0 <  < 360. (ANS = {empty})

Q) If the area of an isosceles triangle is 20, then what is its hypotenuse? (ANS = 2x(10^1/2)

 

[Tide]

1. hint: least common multiple

2. hint: account properly for the trees at the ends!

 

[robert Ihnot]

On the coin toss, if we have 6 tails in 9 tosses, we have an arrangement of tails and heads TTTTTTHHH that could line up in 9!/(6!3!) different ways. (Which is to say they are nine choices for the first place, 8 for the second, etc...but 6 of the choices and 3 of the choices are the same.) The probability of heads is the same as tails 1/2, so that the probability of this event is $$\frac{9!}{6!*3!*2^9}$$