A Picture is Worth 122 Words (adjusted for inflation)

Are you female? Do you often run out of space on your digital camera's memory card from taking all those photos? Wouldn't it be nice to know how much memory you'll need for that next girls' night out? Well fret no further! Introducing Photo-Predictor! This patented new technique will determine just how many photos you'll snap of you and all your friends while you're out hopping those bars. Interested in learning more? Read on!

Betsy has just bought a new shade of mascara and to celebrate she has invited her friends Susie and Mindy out for a night on the town. After searching under her piles of shoes, stacks of Cosmos, and other female stereotypes, Betsy has found her digital camera. The batteries are charged, and she has loaded it with a 128 MB memory card. Let's find out if that will provide enough room...

Betsy must now calculate every possible photo opportunity the three of them will manage to create that night:

To simplify: B = Betsy, S = Susie, M = Mindy

First off, there will be one of each:
B
S
M

Next couples:
BS
BM
SB
SM
MB
MS

Notice that BS is separate from SB. Since Susie can also be on the right of Betsy, it is not satisfactory until there is a photographic record of both poses. Therefore, we are using permutations and not combinations.

And finally all three together:
BSM
BMS
SBM
SMB
MBS
MSB

Adding the above permutations together, Betsy will take at least 15 photos: Small potatoes for 128 MB. But let's see what happens when Betsy's two friends turn into four...

Using the formula:

           n!
n_P_k = --------
        (n - k)!

where we will find the number of permutations of k (girls in photo) taken from n (total number of girls),

           5!
5_P_1 = -------- = 5
        (5 - 1)!

           5!
5_P_2 = -------- = 20
        (5 - 2)!

           5!
5_P_3 = -------- = 60
        (5 - 3)!

           5!
5_P_4 = -------- = 120
        (5 - 4)!

           5!
5_P_5 = -------- = 120  (remember 0! = 1)
        (5 - 5)!

Totaling the numbers above, we arrive at 325 photos!
Uh oh, Betsy. Looks like it's time for an upgrade.

Hopefully, the Photo-Predictor technique has provided a helpful method for solving yet another one of life's woes. Oh and don't forget, each of Betsy's friends will also have a camera. So that makes 1,625 photos the rest of us will be sifting through after they're all posted on Shutterfly the next day.

Until next time, keep on replicating yourselves, girls!