+0

# If i have 90 people coming to an event, with 120 different outfits, what is the chance of two people wearing matching outfits

0
221
1

If i have 90 people coming to an event, with 120 different outfits, what is the chance of two people wearing matching outfits

Guest Mar 24, 2015

#1
+92206
+5

How can 90 people wear 120 different outfits?

I guess you mean that 90 people come and they randomly choose 1 of 120 outfits each.

Let me see...

The number of ways that people can have different outfits (order counts)  is

$$120P90 = 120!/30! \approx 2.5219*10^{166}$$

The number of ways that they can have any outfit = $$120^{90}=1.3376\times 10^{187}$$

The prob that all the outfits are different would be

$$\frac{120!}{30!} \div 120^{90} \approx 1.8855\times 10^{-21}$$

the prob that 2 or more are in the same outfit would be

$$\approx 1-{ 1.8855\times 10^{-21}}=1$$   correct to more than 10 decimal places.

I am not sure of this answer - repeat at own risk.  LOL

Melody  Mar 25, 2015
Sort:

#1
+92206
+5

How can 90 people wear 120 different outfits?

I guess you mean that 90 people come and they randomly choose 1 of 120 outfits each.

Let me see...

The number of ways that people can have different outfits (order counts)  is

$$120P90 = 120!/30! \approx 2.5219*10^{166}$$

The number of ways that they can have any outfit = $$120^{90}=1.3376\times 10^{187}$$

The prob that all the outfits are different would be

$$\frac{120!}{30!} \div 120^{90} \approx 1.8855\times 10^{-21}$$

the prob that 2 or more are in the same outfit would be

$$\approx 1-{ 1.8855\times 10^{-21}}=1$$   correct to more than 10 decimal places.

I am not sure of this answer - repeat at own risk.  LOL

Melody  Mar 25, 2015

### 25 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details