Download Permutations and Factorial Notation Worksheet

Permutations and Factorial Notation Worksheet
1) Evaluate each of the following without a calculator.
a) 5!
b)
20!
18!
c)
10!
9!
d)
10 !
10  9 !
d)
( a  1)!
( a  1)!
2) Simplify each of the following expressions.
a)
n!
( n  1)!
b)
(a  1)!
(a  2)!
c)
a!
(a  2)!
3) On the assembly line at factory, six digit serial numbers are assigned to products according to the
following regulations: only the digits 4 to 9 are used; no digit may be used twice in the same
serial number.
a) Use the Fundamental Counting Principle to calculate the number of possible serial
numbers under the system.
b) Write this answer using factorial notation.
4) Express each of the following in factorial notation.
a) P(7,7)
b) P(m,m)
c) P(7,5)
d) P(a,b)
5) Solve for n, where n N.
a)
( n  1)!
9
n!
b)
n!
 20
(n  2)!
6) List all of the 2-arrangements of the symbols {+, -, x}
7) Determine the following values of n and r in P(n, r) for each of the following.
a)
b)
c)
d)
P(n, r) = 6 x 5 x 4 x 3 x 2 x 1
P(n, r) = 8 x 7 x 6
P(n, r) = 510 x 509 x 508 x 507
P(n, r) = a (a -1)(a – 2)
Answers:
1a) 120
b) 380
c) 10
d) 1
3) 6 x 5 x 4 x 3 x 2 x 1 = 720 b) 6!
5a) 8
b) 5
c) n = 510, r = 4
2a) n
4a) 7!
6) +-, -+, +x, x+, -x, xd) n = a, r = 3
b) a-1
c) a  a
b) m! c)
2
d) a  a
7!
a!
d)
2!
(a  b)!
7a) n = 6, r = 6 b) n = 8, r = 3
2