I was solving this problem:
For a group of 7 people, find the probability that all 4 seasons (winter, spring, summer, fall) occur at least once each among their birthdays, assuming that all seasons are equally likely.
I arrived at the answer: 1 - [4*(3/4)^7 + 6*(2/4)^7 + 4*(1/4)^7].
But the original answer is : 1 - [4*(3/4)^7 - 6*(2/4)^7 + 4*(1/4)^7], and i'm not able to understand why there is a negative sign before the 6*(2/4)^7. Please enlighten me ?