An urn contains 11 numbered balls, of which 6 are red and 5 are white. A sample of 4 balls is to be selected. How many samples contain at least 3 red balls?
Accepted Solution
A:
Answer:The total number of samples that contain at least 3 red balls is 115.Step-by-step explanation:Total number of balls = 11Total number of red balls = 6Total number of white balls = 5A sample of 4 balls is to be selected that contain at least 3 red. It means either 3 out of 4 balls are red or 4 out of 4 ball are red.[tex]\text{Total ways}=\text{Three balls are red}+\text{Four balls are red}[/tex][tex]\text{Total ways}=^6C_3\times ^5C_1+^6C_4\times ^5C_0[/tex]Combination formula:[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Using this formula we get[tex]\text{Total ways}=\frac{6!}{3!(6-3)!}\times \frac{5!}{1!(5-1)!}+\frac{6!}{4!(6-4)!}\times \frac{5!}{0!(5-0)!}[/tex][tex]\text{Total ways}=20\times 5+15\times 1[/tex][tex]\text{Total ways}=115[/tex]Therefore the total number of samples that contain at least 3 red balls is 115.