A man invited 5 friends. He was born in April as also all the invited friends. What is the probability that none of the friends was born on the same day of the month as the host?

Lets say the host was born on 1st April. The probability of this is 1/30. Now, none of the friends should have their D.O.B. as 1st April, hence probability of D.O.B. of any one friend is 29/30 as he can be born on any of the remaining 29 days. However, there are 5 friends, hence, (29/30)^5. However, the host can be born on any of the 30 days. Hence, final answer: [(1/30)*(29/30)^5]*30.

Correct?