John is having computer problems. He noticed that 6 of the 26 letters on his keyboard aren’t working. If John’s computer password consists of 5 distinct letters, what is the probability that John will still be able to type in his password (all 5 letters are working)?

Question

shane_b · Answer

I'm going to take a stab at this one...but I'm no probability expert so someone jump in if you seem something wrong.

You have to multiply the odds of each character working...

1st char: 20/26
2nd char: 19/26
3rd char: 18/26
4th char: 17/26
5th char: 16/26

$$\frac{20}{26}*\frac{19}{26}*\frac{18}{26}*\frac{17}{26}*\frac{16}{26}=15.7\%$$

anonymous · Answer

What the answer key says is that the answer is 3876/16445

shane_b · Answer

3876/16445 is a 23.6% chance...I don't see where my mistake is but maybe someone else will.

anonymous · Answer

Well, here's how they got it. :/

anonymous · Answer

I guess it makes sense now huh?

shane_b · Answer

Ah yes...silly mistake thinking that the 26 would remain constant in each calculation!

shane_b · Answer

I should have realized that he would obviously not try to use the broken keys

shane_b · Answer

If he was blind, then I'm certain my answer would be right :P

anonymous · Answer

Yeah, I waited to look at the solution methods because I like trying to figure it out somewhat. I'm terrible at probability, but I should've figured it out :) lol. THanks for trying though!

shane_b · Answer

I learned something so it wasn't wasted time :)