The String of Beads

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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.

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.


In how many ways can B black beads and (N - B) white beads be arranged on a string?

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  • I 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 (N-B)... I think the correct formula is like the cross genetics of mendel in Biology, 2N...

  • @Michael If you had 2 choices each time, there would be 2N 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.

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