How many ways of assigning 10 people to 3 groups, which group of 3, group of 2 and group of 5.
1. choose 3 from 10
2. choose 2 from 7
which equals 2,520
1. choose 2 from 10
2. choose 3 from 8
which also equals 2,520
or you can think it in this way
there are 10! of ways of assigning it, but there are 3!, 2! and 5! of being overcounted (because there are 3 groups) , so you have to divide them out,
so the equation is 10!/2!3!5!
and the equation extends to is N!/n1!n2!n3!..........nk!
2.
First, dividing 7 of heart, other 12 heart cards and other three 7s.
So divide 16 out of 52, which is 36 left
So choose 4 from 36, which is 58,905
Second, there are 12 cards of heart, 3 7s from other colors
12*3=36
then choosing 3 from 36, which is 7,140
36 * 7140= 257,040
58,905 + 257,040 = 315,945
which are 12% of the choosing 5 from 52 (2,598,960)
awesome!!!
keep learning, Wallace Tiger Baby : )
