Calvin has 3 red juggling pins, 4 blue juggling pins, 5 white juggling pins, and 6 green juggling pins. How many ways can he give a set of 3 juggling pins to Dan?
18! / 3!4!5!6!*3!
The question should be about the number of ways he can choose 3 pins. Who knows how he gives them away?
I am not sure how to solve that?
To solve this problem, we can use combinations, which is a way of selecting items from a larger set without regard to the order in which they are arranged.
In this case, Calvin has a total of 3 + 4 + 5 + 6 = 18 juggling pins. We want to find the number of ways he can give a set of 3 juggling pins to Dan.
To calculate combinations, we use the formula: C(n, r) = n! / (r!(n-r)!), where n represents the total number of items and r represents the number of items chosen.
In this case, n = 18 (the total number of juggling pins) and r = 3 (the number of pins to be chosen).
Therefore, the number of ways Calvin can give a set of 3 juggling pins to Dan is:
C(18, 3) = 18! / (3!(18-3)!) = 18! / (3! * 15!) = (18 * 17 * 16) / (3 * 2 * 1) = 816.
So, Calvin can give a set of 3 juggling pins to Dan in 816 different ways.