Evaluate C(12,10).
C(n,r)=n!/(n-r)!r!
=12!/(12-10)!10
=12!/2!2
=12*11/2*1
=66
correct.
To evaluate C(12,10), we can use the formula for combinations:
C(n,r) = n! / (r!(n-r)!)
Here, n represents the total number of items we have to choose from, and r represents the number of items we want to choose.
To find C(12,10), we substitute n=12 and r=10 into the formula:
C(12,10) = 12! / (10!(12-10)!)
= 12! / (10! * 2!)
Next, we simplify the expression.
We know that 12! is equal to 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.
We also know that 10! is equal to 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.
And finally, we know that 2! is equal to 2 * 1.
Substituting these values into the expression:
C(12,10) = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) * (2 * 1))
Canceling out common factors in the numerator and denominator:
C(12,10) = (12 * 11) / (2 * 1)
Evaluating the expression:
C(12,10) = 132 / 2
= 66
Therefore, C(12,10) is equal to 66.