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

Answer:

$\frac{969}{1771}$

Step-by-step 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 = $\frac{^{19}C_3}{^{23}C_3}$

$=\frac{\frac{19!}{3!16!}}{\frac{23!}{3!20!}}$

$=\frac{969}{1771}$