Samantha has five objects weighing 1kg,2kg,3kg,4kg and 5kg. If she weighs them two at a time, how many different weighs can she get?
To find out how many different weights Samantha can get by weighing the objects two at a time, we can use the combination formula.
The combination formula is given by:
nCr = n! / (r! * (n-r)!)
where n is the total number of objects and r is the number of objects we are choosing at a time.
In this case, Samantha has five objects, so n = 5.
She is weighing them two at a time, so r = 2.
Using the combination formula:
nCr = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2 * 1 * 3!)
= (5 * 4) / (2 * 1) // 3! cancels out
= 20 / 2
= 10
Therefore, Samantha can get 10 different weights by weighing the objects two at a time.
To find out how many different weights Samantha can get, we need to consider the different combinations of objects that she can weigh together.
When Samantha weighs two objects at a time, she can choose any two objects from the five objects she has. To calculate the number of combinations, we can use the formula for calculating combinations:
nCr = n! / (r!(n-r)!)
Where n represents the total number of objects and r represents the number of objects chosen at a time.
In this case, n = 5 (as Samantha has five objects), and r = 2 (as she is weighing two objects together).
So, the number of different weighs Samantha can get is:
5C2 = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3!) / (2!(3 * 2 * 1))
= (5 * 4) / (2 * 1)
= 10
Therefore, Samantha can get 10 different weighs by weighing two objects at a time.
There are 5C2 = 10 ways to select the weights. However, there are some duplicates, such as
1+5 and 2+4
I suppose you can find how many, and subtract them from 10.