Seven chits are numbered 1 to 7. Three are drawnone by one with replacements. The probability thatthe least number on any selected chit is 5, isa)1-(2/7)4b)(2/7)4c)(3/7)3d)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Problem Analysis:
We have seven chits numbered from 1 to 7. We need to find the probability that the least number on any selected chit is 5.

Solution:
Let's consider the different possibilities to select three chits one by one with replacement.

1. The least number on the selected chits is 5:
In this case, we can have the following combinations:
- (5, 5, 5)
- (5, 5, 6)
- (5, 5, 7)
- (5, 6, 6)
- (5, 6, 7)
- (5, 7, 7)
There are 6 such combinations.

2. The least number on the selected chits is not 5:
In this case, we can have the following combinations:
- (1, 1, 1)
- (1, 1, 2)
- (1, 1, 3)
- (1, 1, 4)
- (1, 1, 5)
- (1, 1, 6)
- (1, 1, 7)
- (1, 2, 2)
- (1, 2, 3)
- (1, 2, 4)
- (1, 2, 5)
- (1, 2, 6)
- (1, 2, 7)
- (1, 3, 3)
- (1, 3, 4)
- (1, 3, 5)
- (1, 3, 6)
- (1, 3, 7)
- (1, 4, 4)
- (1, 4, 5)
- (1, 4, 6)
- (1, 4, 7)
- (1, 5, 5)
- (1, 5, 6)
- (1, 5, 7)
- (1, 6, 6)
- (1, 6, 7)
- (1, 7, 7)
- (2, 2, 2)
- (2, 2, 3)
- (2, 2, 4)
- (2, 2, 5)
- (2, 2, 6)
- (2, 2, 7)
- (2, 3, 3)
- (2, 3, 4)
- (2, 3, 5)
- (2, 3, 6)
- (2, 3, 7)
- (2, 4, 4)
- (2, 4, 5)
- (2, 4, 6)
- (2, 4, 7)
- (2, 5, 5)
- (2, 5, 6)
- (2, 5, 7)
- (2, 6, 6)
- (2, 6, 7)
- (2, 7, 7)
- (3, 3, 3)
- (3, 3, 4)
- (3, 3,

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