Question

Twenty beads are strung in a circle. 14 are brown and 6 are red. How many ways can the beads
be strung in a circle if a clasp is used?

Answer 1

There are 20 beads in total. Assume they are all unique. The number of ways they can be arranged is 20!

The number of ways 14 brown beads can be arranged is 14! and
the number of ways 6 red beads can be arranged is 6!

Here we are interested in the combination and not the permutations because all brown beads are alike and all the red beads are alike. Therefore, the number of unique combinations are: 20! / { 14! * 6! }

Simplify.

Answer 2

but the answer is 19380

Answer 3

Maybe we need to divide the above by 2 because beads arranged from left to right and right to left will look the same when reversed.

20! / { 14! * 6! } = 38,760

38,760 / 2 = 19,380.

Answer 4

I see, thank you!!!