SME
Grade 10 Math · Problem type
Permutations: order matters
Use this for “In how many ways can 8 runners take gold, silver and bronze?”
Diagram
3 places in order: 8 × 7 × 6 = 336 ways.
This is an example. Type your own values to start a new problem.
P(
n
,
r
)
=
P
Formulas
P
=
n
!
(
n
−
r
)!
336
=
8!
(8 − 3)!
Assumptions
•
The first place can go to any of the n; each later place has one fewer choice.
•
So P(n, r) = n × (n − 1) × … for r places = n! ÷ (n − r)!.
•
Order matters: gold to Ana and silver to Ben differs from the other way round.
Step-by-step
WE KNOW
n = 8, r = 3
FIND
ways (P)
Step 1 · Find ways (P)
Use P = n! ÷ (n − r)!
n
×
(
n
−
1)
×
…
for
r
places:
n
!
with
the
unused
(
n
−
r
)!
divided
out.
P
=
8!
(8 − 3)!
P
=
8
×
7
×
6
P
=
336
Check
Put the numbers back in. Both sides should match.
336
=
8!
(8 − 3)!
✓
Topic check
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Sample spaces, the addition rule, permutations and combinations
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