evaluate 60C3/15C3
To evaluate 60C3/15C3, we need to use the formula for combinations:
nCr = n!/(r!(n-r)!)
where n is the total number of elements, r is the number of elements chosen, and ! denotes the factorial function, which means the product of all positive integers up to that number.
In this case, we have:
60C3 = 60!/(3!(60-3)!) = 60!/(3!57!) = (60x59x58)/(3x2x1) = 34,860
15C3 = 15!/(3!(15-3)!) = 15!/(3!12!) = (15x14x13)/(3x2x1) = 455
Therefore, 60C3/15C3 = 34,860/455 = 76.61538462 (rounded to 8 decimal places).
mmmhhh?
60C3 = 34220
15C3 = 455
so 34220/455 = 6844/91= appr 75.21 rounded to 2 decimals
You are correct. I apologize for the mistake in my calculation.
60C3 = 34220
15C3 = 455
Therefore, 60C3/15C3 = 34220/455 = 75.21 (rounded to 2 decimal places).
Thank you for pointing out the error.
To evaluate the expression 60C3/15C3, we need to first calculate the values of 60C3 and 15C3, and then divide them.
To calculate the combination values, we use the formula for combination:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items being chosen.
Let's start with 60C3:
60C3 = 60! / (3!(60-3)!)
To simplify the calculation, we can cancel out some of the terms:
60! = 60 * 59 * 58 * 57!
3! = 3 * 2 * 1
Now, let's substitute these values back into the formula:
60C3 = (60 * 59 * 58 * 57!) / (3 * 2 * 1 * (57!) )
Simplifying further:
60C3 = 60 * 59 * 58 / (3 * 2 * 1)
Now let's calculate 15C3:
15C3 = 15! / (3!(15-3)!)
Again, we can cancel out some terms:
15! = 15 * 14 * 13 * 12!
3! = 3 * 2 * 1
Substituting the values:
15C3 = (15 * 14 * 13 * 12!) / (3 * 2 * 1 * (12!))
Simplifying:
15C3 = 15 * 14 * 13 / (3 * 2 * 1)
Now that we have the values for 60C3 and 15C3, we can evaluate the expression:
60C3 / 15C3 = ( 60 * 59 * 58 / (3 * 2 * 1) ) / ( 15 * 14 * 13 / (3 * 2 * 1) )
Since the denominators are equal, we can cancel them out:
60C3 / 15C3 = (60 * 59 * 58) / (15 * 14 * 13)
Now we can simplify the fraction:
60C3 / 15C3 = 60 * 59 * 58 / 15 * 14 * 13
Doing the multiplication:
60C3 / 15C3 = 205,920 / 3,570
And finally, performing the division:
60C3 / 15C3 = 57.79