Answer:
[tex]\frac{969}{1771}[/tex]
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 = [tex]^{23}C_3[/tex]
Number of ways of choosing 3 non grape juice cans = [tex]^{19}C_3[/tex]
Hence, the probability of selecting no grape juice = [tex]\frac{^{19}C_3}{^{23}C_3}[/tex]
[tex]=\frac{\frac{19!}{3!16!}}{\frac{23!}{3!20!}}[/tex]
[tex]=\frac{969}{1771}[/tex]
