There are 6 dancers in a program. Each dancer will preform a short dance with each of the other dancers before the program is over. How many dancers will there be
Your problem states that there are 6 dancers.
Do you need to know how many dances there will be?
Yes how many dances
There should be 15 dances.
ms.sue could you please answer my question i previousl posted
How did you come up with that #?
Dancer 1 dances with dancers 2, 3, 4, 5, 6
2: 3, 4, 5, 6,
3: 4, 5, 6
4: 5, 6
5: 6
Understood thanks!
You're welcome.
combinations of 5 taken 2 at a time
c(5,2) = 5!/[3!*2!] = 5*2 = 10
To determine the number of dance pairs that can be formed, we need to calculate the number of combinations.
First, let's compute the number of pairs that can be formed between the 6 dancers. To find the number of combinations, we can use the formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items chosen at a time, and ! denotes the factorial operation.
In this case, we want to find the number of combinations for pairs, so r equals 2. Plugging in the values:
nCr = 6! / (2!(6-2)!)
= 6! / (2!4!)
To calculate this further, let's compute the factorials:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
2! = 2 x 1 = 2
4! = 4 x 3 x 2 x 1 = 24
Now we can substitute these values back into the initial formula:
nCr = 720 / (2 x 24)
= 720 / 48
= 15
Therefore, there will be 15 dance pairs among the 6 dancers.