zurich wrote:
Quote:
The probability of winning is 40% = 40/100 = 2/5.
The probability of NOT winning is 60% = 3/5.
P(WWWNN)=5!3!2!∗(25)3∗(35)2=144625≈23 (we multiply by 5!3!2!, because WWWNN scenario can occur in several ways: WWWNN, WWNWN, WNWWN, NWWWN, ... the # of such cases basically equals to the # of permutations of 5 letters WWWNN, which is 5!3!2!).
Answer: B.
Why do we have to divide by 3!2!? I thought that simply multiply it by 5! as it is permutation.
Hi Zurich,
In this case the order of the people selecting the notes does not matter. It can be looked at as a combination, instead of a permutation. The number of ways to select 3 winners out of 5 is given by 5C3 = \(\frac{5!}{3!2!}\)
It is mathematically the same as saying we will find the number of permutations of 5 people, but when there are 3 identical and 2 identical people in the group. In this case, we must divide the permutation of 5 people, 5!, by the number of arrangements of each of the identical elements, 3! and 2!.
This again equals \(\frac{5!}{3!2!}\)
The only difference is the way we explain it. Either we are choosing 3 out of 5 where the order doesn't matter, or we are arranging 3 identical and 2 identical items in a row. It works out to the same thing.
I hope that helps to clear it up!