b) For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
 alt="b)
For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table.
Silver
White
Black
Korea
33
34
35
Japan
23
24
America
16
25
34
Germany
19
16
32
One car is selected at random from this group. Find the probability that the selected car is
(1) a black or white car manufactured in Korea.
(11) not manufactured in Japan.
(iii) is a white car, given that it was manufactured in America.
(iv) Are the events 'Korea' and 'Black' Mutually Exclusive? Justify your response.
(v) Are the events 'Korea' and 'Black' Independent? Justify your response
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