Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

The probability that out of 10 persons, all born in April, at least two have the same birthday is:

Options:

$\frac{{^{30}C}_{10}}{(30)^{10}}$

$1-\frac{{^{30}C}_{10}}{30!}$

$\frac{(30)^{10}-{^{30}C}_{10}}{(30)^{10}}$

None of these

Correct Answer:

None of these

Explanation:

Total no. of ways to allot 30 days to 10 people = 3010

Allot 10 days to 10 people as birthday = 30C10 × 10!

P(at least 2 have same birthday) = 1 - P (no one has same birthday) = $1-\frac{{^{30}C}_{10}×10!}{30^{10}}$