 Intro to Combinations and Permutations
 Permutations with Repetition
 Permutations without Repetition
 Permutations Formula

License Plates  Android Lock Screen
 Tigers and Bears  Oh My

Combination without Repetition  Combination Formula
 Combining Combinations

The String of Beads  Anagrams
 Combinations with Repetition I
 Combinations with Repetition II
The String of Beads
The next few challenges will cover some more advanced cases. Just as there can be many ways to travel to a destination, there can be different ways to solve a problem. Often, you can convert a problem into a simpler one by understanding what is being asked.
Challenge
You need to make a string of N beads. You must use B black beads and the rest of the beads need to be white. In how many different ways can you arrange the beads? Note: Please write a formula to solve the problem in terms of B and N (capitalized). You can use standard math notation in your formula, including "!", choose and permute.
Challenge
In how many ways can B black beads and (N  B) white beads be arranged on a string?
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Comments
Michael
Sep 2, 6:30 AMI don't agree with the answer, ex: if we have 3 N on string, the combination of the balls is NC3+NC2+NC1+NC0 because NC3 is BBB, NC2 are BBW,BWB,WBB, NC1 are WWB,WBW,BWW, and NC0 is WWW... nb: W is (NB)... I think the correct formula is like the cross genetics of mendel in Biology, 2^{N...}
Learneroo
Sep 17, 12:46 PM@Michael If you had 2 choices each time, there would be 2^{N} possible permutations. But you're given a set number of black and white beads, so eventually you will only be able to use 1 color.
You could make a tree to determine the possibilities for a specific example, but a simpler solution is to use Choose.