combinations vs permutations questions
hi, i'm new here and am looking for some help!
this was in a chapter that uses permutations and combinations...but i cant figure out how to get it. it's just for practice, and i know the answers (the probability of 5 out of 52 is higher)...but i'd like to find out why.
Are the odds of winning in a lotto drawing higher when picking 6 numbers out of 49 vs. 5 numbers out of 52? calculate each probability.
This one's more wordy but I'm also confused:
In June 2004, Canada introduced a change in its lottery that violated the usual convention that the smaller the probability of an event, the bigger the prize. In this lottery, participants have to guess six numbers from 1 to 49. Six numbers between 1 and 49 are then drawn at random, plus a seventh "bonus number."
a) a fifth prize of $10 goes to those who correctly guess exactly three of the six numbers, but do not guess the bonus number. Find the probability of winning fifth prize.
b) A sixth prize of $5 goes to those who correctly guess exactly 2 of the six numbers plus the bonus number. Find the probability of winning sixth prize, and compare this with the probability of winning fifth prize.
Again, I know the answer for a) is .01642 and b) is .01231...but if someone could show me HOW to get to it that'd be great!
Thanks! This seems like a great community :)