The package claims an astounding 4,194,304 different combinations are possible:
"It's a mathematical fact that you can play with 'Changeable Charlie' eight hours a day, five days a week, fifty-two weeks a year, making one change a minute, and not repeat yourself in over thirty-three years! If you want to know how mathematicians figured this out, send us a postal card with your name and address. We'll be delighted to show you how it's done."
Alas, I have to go to work each day, and so have been unable to test this claim.
This 1948 set features fantastic caricatures.
Changeable Charlie was so popular, it spawned a sequel called Changeable Charlie's Aunt. This set dates from 1960.