how many different bracelets from 7 white beads and 2 gray ones.
I don't understand the question. Are you asking how many different bracelets you can make by having 7 white beads and 2 gray beads?
If you do, do you have to use all 9 beads?
Please expand on your question so it is easier to help.
Yes
To find the number of different bracelets that can be made from 7 white beads and 2 gray ones, we can use the concept of permutations.
Step 1: Calculate the total number of beads (n) in the bracelet by adding the number of white beads (w) and gray beads (g): n = w + g = 7 + 2 = 9.
Step 2: Now, we need to calculate the total number of ways to arrange these beads in a straight line without considering the circular nature of the bracelet. This can be done using the formula for permutations of distinguishable objects:
Permutations = n!
---------------
w! * g!
Where "!" denotes the factorial function.
For our case, substituting the values, we have:
Permutations = 9! / (7! * 2!)
Step 3: Simplify the expression:
Permutations = (9 * 8 * 7!) / (7! * 2)
The "7!" term cancels out in the numerator and denominator, giving:
Permutations = (9 * 8) / 2
Step 4: Calculate the final number of different bracelets:
Permutations = 72 / 2 = 36
Therefore, there are 36 different bracelets that can be made from 7 white beads and 2 gray ones.