An ice chest contains 4 cans of apple juice, 8 cans of grape juice, 6 cans of orange juice, and 5 cans of pineapplejuice. Suppose that you reach into the container and randomly select three cans in succession. Find theprobability of selecting no grape juice.
A) $\frac { 65 } { 253 }$
B) $\frac { 1125 } { 3542 }$
C) $\frac { 2730 } { 12167 }$
D) $\frac { 8 } { 253 }$

Question

An ice chest contains 4 cans of apple juice, 8 cans of grape juice, 6 cans of orange juice, and 5 cans of pineapplejuice. Suppose that you reach into the container and randomly select three cans in succession. Find theprobability of selecting no grape juice. 
A) $\frac { 65 } { 253 }$
B) $\frac { 1125 } { 3542 }$
C) $\frac { 2730 } { 12167 }$
D) $\frac { 8 } { 253 }$

Quizplus · Accepted Answer

The total number of ways to select 3 cans from 23 (4 apple + 8 grape + 6 orange + 5 pineapple = 23) is $\binom{23}{3}$. To select no grape juice, we choose from the 15 non-grape juice cans (4 apple + 6 orange + 5 pineapple = 15), which is $\binom{15}{3}$. The probability is $\frac{\binom{15}{3}}{\binom{23}{3}} = \frac{65}{253}$.

An Ice Chest Contains 4 Cans of Apple Juice, 8 65253\frac { 65 } { 253 }25365​

An Ice Chest Contains 4 Cans of Apple Juice, 8 $\frac { 65 } { 253 }$