There are 4 mangoes, 3 apples. 2 oranges and 1 each of 3 other varieties of fruits. The number of ways of selecting atleast one fruit of each kind isa)10!b)9!c)4!d)none of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

4C1×3C1×2C1×1C1×1C1×1C1=24
=4!

Answer

Explanation:

Given:
- 4 mangoes
- 3 apples
- 2 oranges
- 1 each of 3 other varieties of fruits

Number of ways to select at least one fruit of each kind:
To ensure that at least one fruit of each kind is selected, we can choose one fruit from each type and then choose any remaining fruits from the rest.

Calculation:
- Number of ways to select one fruit each from 4 mangoes, 3 apples, and 2 oranges = 4 * 3 * 2 = 24 ways
- Number of ways to choose the remaining 3 fruits from 3 other varieties = 3! = 6 ways

Total number of ways:
- Total number of ways = 24 * 6 = 144 ways

Final Answer:
The number of ways of selecting at least one fruit of each kind is 4!.

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