Answer:
Step-by-step explanation:
(a)
Total number of members are (2 + 3 + 5 + 2) = 12.
From these 12 members 4 can be chosen in [tex]^{12}C_4 = \frac{12\times11\times10\times9}{4\times6} = 495[/tex] ways.
All the nationalities will be there only when one from each nationality will be there.
Hence, the required answer is [tex]\frac{2\times3\times5\times2}{495} = \frac{4}{33}[/tex].
(b)
There will be no Italians, hence all 4 should be chosen from (12 - 5) = 7 people.
From, 7 people, 4 can be chosen in [tex]^7C_4 = \frac{5\times6\times7}{6} = 35[/tex] ways.
Hence, in this case, the probability will be [tex]\frac{35}{495} = \frac{7}{99}[/tex].
