Hi

Bunuel Can you help me get what is wrong in the following solution?

Hi All

Can someone help me with the following question?

I can solve it with the 1-complement approach but i want to solve for individual cases and add them up.

Case 1. Two people born under the same star.

SSDDD S stands for the same star sign and D for a different star sign.

12/12* 1/12* 11/12* 10/12* 9/12 * 5!/3!*2! =9900/12^4

5 stars can be arranged in 5! ways. we need to dived by 3! because the arrangement of three stars has already been counted and divide by 2 to remove the two same star signs eg AA. Is the reasoning correct here?

Similarly Other cases

SSSDD

12/12 *1/12* 1/12*11/12 * 10/12 * 5!/3!*2! = 1100/12^4

SSSSD

12/12 *1/12* 1/12* 1/12 * 11/12 * 5!/4! = 55/12^4

SSSSS

12/12 *1/12* 1/12* 1/12 * 1/12 = 1/12^4

Adding up all these 4 cases yields 11056/12^4 = 0.53 but that is not the correct answer. Please help me get the mistake. Thank you