Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle
Answer:
86400 ways
Step-by-step explanation:
Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.
Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.
After picking the places for the women, we will now fill each gap between two women with a man.
We have 6 men. Thus, number of ways to arrange the men is 6!
Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways
Answer:
242
Step-by-step explanation:
Simplify the following:
11 ((9^2 - 5^2)/2^2 + 8)
Hint: | Evaluate 2^2.
2^2 = 4:
11 ((9^2 - 5^2)/4 + 8)
Hint: | Evaluate 5^2.
5^2 = 25:
11 ((9^2 - 25)/4 + 8)
Hint: | Evaluate 9^2.
9^2 = 81:
11 ((81 - 25)/4 + 8)
Hint: | Subtract 25 from 81.
| 7 | 11
| 8 | 1
- | 2 | 5
| 5 | 6:
11 (56/4 + 8)
Hint: | Reduce 56/4 to lowest terms. Start by finding the GCD of 56 and 4.
The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:
11 (14 + 8)
Hint: | Evaluate 14 + 8 using long addition.
| 1 |
| 1 | 4
+ | | 8
| 2 | 2:
11×22
Hint: | Multiply 11 and 22 together.
| 2 | 2
× | 1 | 1
| 2 | 2
2 | 2 | 0
2 | 4 | 2:
Answer: 242
Answer:
(2^3)^2/2^3X2^2 = 6/4 = 3/2
Step-by-step explanation:
(2^3)^2 = 6^2 = 36
2^3 X 2^2 = 6 X 4 = 24
