Sara has 6 necklaces, but her mother will only allow her to wear two at a time. How many different ways can Sara wear two necklaces?
A. 30
B. 15
C. 360
D. 12
6C2 = (6*5)/(1*2) = 15
To find the number of different ways Sara can wear two necklaces out of her collection of 6, we need to use the combination formula.
The formula to calculate the number of combinations of selecting r items from a set of n items is given by:
nCr = n! / (r! * (n-r)!)
In this case, n = 6 (the number of necklaces Sara has) and r = 2 (the number of necklaces she can wear at a time).
So, we can calculate the number of combinations as follows:
6C2 = 6! / (2! * (6-2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / 2!
= (6 * 5) / (2 * 1)
= 30 / 2
= 15
Therefore, there are 15 different ways Sara can wear two necklaces.
The answer is B. 15.
To determine the number of different ways Sara can wear two necklaces out of her 6 necklaces, we can use the concept of combinations.
The formula for combinations is given by nCr = (n!)/(r!(n-r)!), where n is the total number of items and r is the number of items chosen at a time.
In this case, Sara has 6 necklaces (n=6) and she wants to wear 2 necklaces (r=2). Plugging these values into the combination formula, we have:
nCr = (6!)/(2!(6-2)!)
= (6!)/(2!4!)
= (6x5x4x3x2x1)/((2x1)(4x3x2x1))
= (720)/(2x24)
= 720/48
= 15
Therefore, there are 15 different ways Sara can wear two necklaces.
The correct answer is B. 15.
Sara has 6 necklaces, but her mother will only allow her to wear two at a time. How many different ways can Sara wear two necklaces?
A. 30
B. 15
C. 360
D. 12