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The given table shows the possible food choices for lunch. How many different types of lunch can be made each including $1$ type of soup, $1$ type of sandwich and 1type of salad?
Lunch choices
Soup Sandwich Salad
Chicken Cheese vegetable
Tomato Paneer fruit

A). $2$
B). $3$
C). $6$
D). $8$

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Last updated date: 25th Jul 2024
Total views: 349.5k
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Answer
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Hint: In our question, there are different types of lunch choices. That is, there are two types of soup (Chicken soup and tomato soup), two types of sandwich (Cheese sandwich and Paneer sandwich) and two types of salad (vegetable salad and fruit salad).
Our question is to find the number of possible types of lunch that can be prepared including $1$ type of soup, $1$ type of sandwich and 1type of salad.
Now, we shall name the lunch choices by their first letter for our convenience.
Let CI be the chicken soup,
T be the tomato soup,
CE be the cheese sandwich,
P be the Paneer sandwich,
V be the vegetable salad,
F is the fruit salad.

Complete step-by-step solution:
We have considered the lunch choices as follows.
Let CI be the chicken soup,
T be the tomato soup,
CE be the cheese sandwich,
P be the Paneer sandwich,
V be the vegetable salad,
F is the fruit salad.
Our question is to find the number of possible types of lunch that can be prepared including $1$ type of soup, $1$ type of sandwich and 1type of salad.
Now, let us take the chicken soup. And then we need to combine the chicken soup with two types of Sandwich and also with two types of salad.
So we have the following possible outcomes.
CI CE V, CI CE F, CI P V, CI P F
Hence there are $4$ possible lunch choices when we consider chicken soup.
Now, let us take the tomato soup. And then we need to combine the tomato soup with two types of sandwich and also with two types of salad.
So we have the following possible outcomes.
T CE V, T CE F, T P V, T P F
Hence there are $4$ possible lunch choices when we consider tomato soup.
Now, we need to add the above possible lunch choices.
So, we have $8$ possible lunch choices.
Hence, option D is correct.

Note: But this method is difficult for calculating the number of possible outcomes that are more than two choices. We shall use the tree method and \[2\]-way table method. Among these methods, the tree method is preferred.