If the probability of Sita getting selected to a school is

It's much better to calculate the probability of the opposite event, which would be that Sita will be rejected by all three schools, and subtract that value from 1: \(P=1-(\frac{4}{5})^3=\frac{61}{125}\).

Direct approach:
The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:

1. She is selected by only one school: \(P(SRR)=\frac{3!}{2!}*\frac{1}{5}*\frac{4}{5}*\frac{4}{5}=\frac{48}{125}\) (S stands for selected and R stands for rejected). We are multiplying by \(\frac{3!}{2!}\), since SRR scenario can occur in several ways: SRR, RSR, RRS, (so \(\frac{3!}{2!}\) is # of permutations of 3 letters SRR out of which 2 R's are identical);

2. She is selected by only two school: \(P(SSR)=\frac{3!}{2!}*\frac{1}{5}*\frac{1}{5}*\frac{4}{5}=\frac{12}{125}\), the same reason of multiplying by \(\frac{3!}{2!}\);

3. She is selected by all three school: \(P(SSS)=(\frac{1}{5})^3=\frac{1}{125}\), we are not multiplying this time since SSS can occur only in one way.

So \(P=\frac{48}{125}+\frac{12}{125}+\frac{1}{125}=\frac{61}{125}\).

Answer: C.

Hope it's clear.
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BB's answers are 99.99999 times crystal clear..

thanks for the explanation BB

We can use the equation:

P(selected into at least 1 school) = 1 - P(selected to no schools)

P(selected to no schools) = 4/5 x 4/5 x 4/5 = 64/125

Thus,

P(selected into at least 1 school) = 1 - 64/125 = 61/125

Answer: C
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