Please help me with my algebra homework as soon as possible please

Question

Each of 5 boys randomly chooses a watch from 12 different styles. What is the probability that at least 2 boys choose the same type of watch?

 

A.) ≈ 0.5387

B.) ≈ 0.7387

C.) ≈ 0.3819

D.) ≈ 0.6181

help

 

Answer 1

I have thought about this some more.

The solution assumes that there is no collusion among the boys, i.e. the choices are independent.

This is a balls into boxes problem, where the watch styles are the boxes and the boys are the balls.

There are ₁₂C₅ * 5! ways in which each boy picks a different watch (12 boxes, 5 balls, no box multiply filled)=792*120=95040

There are 12⁵ ways of distributing 5 balls in 12 boxes=248832.

The required probability then is 1-(95040/248832)=.6181