Evaluate the quantity.
4 · P(4, 4) · C(9, 5)
what is
4(4!/(4-4)! ( 9!/(4!5!) ?
To evaluate the given expression, we need to calculate the values of P(4, 4) and C(9, 5) first.
P(4, 4) represents the permutation of 4 objects taken all at a time. It is calculated using the formula:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects taken at a time.
In this case, P(4, 4) would be:
P(4, 4) = 4! / (4 - 4)!
= 4! / 0!
= 4! / 1
= 4
Next, C(9, 5) represents the combination of 9 objects taken 5 at a time. It is calculated using the formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, C(9, 5) would be:
C(9, 5) = 9! / (5! * (9 - 5)!)
= 9! / (5! * 4!)
= (9 * 8 * 7 * 6 * 5!) / (5 * 4!)
= (9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)
= 3024 / 120
= 25.2
Finally, we can evaluate the entire expression by multiplying 4, P(4, 4), and C(9, 5):
4 · P(4, 4) · C(9, 5)
= 4 · 4 · 25.2
= 403.2
Therefore, the value of the given expression is 403.2.