Respuesta :
Answer:311740
Step-by-step explanation:
Given
There are 14 blue birds and 11 robins
We have to choose 7 members such that there are more blue birds than robins
This can be possible in 4 ways i.e.
7 BB,6 BB and 1 R, 5 BB 2 R,4 BB 3 R
Therefore total no of ways are
[tex]=^{14}C_7+^{14}C_6\times ^{11}C_1+^{14}C_6\times ^{11}C_2+^{14}C_4\times ^{11}C_3[/tex]
[tex]=311740\ ways[/tex]
Answer:
Step-by-step explanation:
number of bluebirds = 14
number of robins = 11
Total selected birds = 7
There are several ways to select the birds
(1) Selection of 7 blue birds out of 14 = [tex]^{14}C_{7}=\frac{14!}{7!\times 7!}=6864[/tex]
(2) selection of 6 blue birds and 1 robin = [tex]^{14}C_{6}\times ^{11}C_{1}=\frac{14!}{6!\times 8!}\times \frac{11!}{1!\times 10!}=33033[/tex]
(3) selection of 5 blue birds and 2 robins = [tex]^{14}C_{5}\times ^{11}C_{2}=\frac{14!}{5!\times 9!}\times \frac{11!}{2!\times 9!}=110110[/tex]
(4) selection of 4 blue birds and 3 robins = [tex]^{14}C_{4}\times ^{11}C_{3}=\frac{14!}{4!\times 10!}\times \frac{11!}{3!\times 8!}= 165165[/tex]
So, the total number of selections to have more blue birds than robins =
= 6864 + 330330 + 110110 + 165165 = 612469
