6 people each choose a number at random from 1 to 4. What is the probability that at least five people choose the same number?
I'll pretend you are rolling 6 four sided dice
say you roll 5 'ones' there are 6 ways to do this
5 twos 6 ways
5 threes 6 ways
5 fours 6 ways
so 24 ways to roll five-of- a kind
now you can also roll 6 of a kind four ways : four ones four twos four threes or four fours
so 24 ways to roll 5 of a kind + 4 ways to roll 6 of a kind = 28 rolls
the number of possible rolls is 46 = 4096
28 / 4096 = 7/1024 = 0.0068359375 (I think)
