Question

An ice chest contains six cans of apple​ juice, four cans of grape​ juice, five cans of orange​ juice, and eight cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

Answer 1

`(969)/(1771)`

Explanation:

Given,

Cans of apple juice = 6,

Cans of grape juice = 4,

Cans of orange juice = 5,

Cans of mango juice = 8,

Thus, the number of cans with no grape juice = 6 + 5 + 8 = 19,

While the total cans = 6 + 4 + 5 + 8 = 23,

Number of ways of choosing any three cans =
`^(23)C_3`

Number of ways of choosing 3 non grape juice cans =
`^(19)C_3`

Hence, the probability of selecting no grape juice =
`(^(19)C_3)/(^(23)C_3)`

`=((19!)/(3!16!))/((23!)/(3!20!))`

`=(969)/(1771)`