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 : )