##### in a group of 6 people there are 3 indians and 3 chinese.How many subset can be created such that there are atleast 1 indian in each subset?

in a group of 6 people there are 3 indians and 3 chinese.How many subset can be created such that there are atleast 1 indian in each subset?

ans 56?

1 indian and (0 or 1 or 2 or 3 ) Chinese=>

^{3}C_{1}*(^{3}C_{0}+^{3}C_{1}+^{3}C_{2}+^{3}C_{3})=3*8=24

2 indian and (0 or 1 or 2 or 3 ) Chinese=>

^{3}C_{2}*(^{3}C_{0}+^{3}C_{1}+^{3}C_{2}+^{3}C_{3})=3*8

3 indian and (0 or 1 or 2 or 3 ) Chinese=>

^{3}C_{3}*(^{3}C_{0}+^{3}C_{1}+^{3}C_{2}+^{3}C_{3})=1*8

Answer: 24+24+8=56

thx for nice explanation