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Question 22: According to birth registration data available with the South Delhi Municipal Corporation,7 babies were born in a particular week in a private hospital. What is the probability that three babies were born on the same day of the week?

- \\frac{1800}{7^5})
- \\frac{1600}{7^7})
- \\frac{2100}{7^7})
- \\frac{2400}{7^5})

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Each baby can be born on any of the 7 days and so for 7 babies the total sample size becomes 7^7

Further, to find 3 babies born on the same day we select 3 babies out of 7 in 7C3 ways.

And these babies can be born on any of the 7 days, which can be selected in 7 ways.

The remaining 4 babies must be born on 4 different days out of the remaining 6 days.

This can be done in in 6C4 ways, and the babies can be arranged in these 4 days in 4! Ways.

So our final calculation becomes:

\\frac{7C3 × 7 × 6C4 × 4!}{7^{7}})

On solving we get

\\frac{1800}{7^5})

The question is **"What is the probability that three babies were born on the same day of the week? **

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