SME
Grade 10 Math · Problem type
Combinations: order doesn’t matter
Use this for “In how many ways can a committee of 3 be chosen from 8 people?”
Diagram
3 places in order: 8 × 7 × 6 = 336 orders.
Each
group
of
3
comes
in
3!
=
6
orders:
336
6
=
56
groups.
This is an example. Type your own values to start a new problem.
C(
n
,
r
)
=
C
Formulas
C
=
n
!
(
n
−
r
)! ×
r
!
56
=
8!
(8 − 3)! × 3!
Assumptions
•
Fill r places in order, then divide by the r! orders each group can be listed in.
•
So C(n, r) = n! ÷ ((n − r)! × r!).
•
Order doesn’t matter: a committee of Ana and Ben is the same as Ben and Ana.
Step-by-step
WE KNOW
n = 8, r = 3
FIND
groups (C)
Step 1 · Find groups (C)
Use C = n! ÷ ((n − r)! × r!)
The
ordered
count,
n
!
(
n
−
r
)!
,
divided
by
the
r
!
orders
of
each
group.
C
=
8!
(8 − 3)! × 3!
C
=
8 × 7 × 6
3 × 2 × 1
C
=
336
6
C
=
56
Check
Put the numbers back in. Both sides should match.
56
=
8!
(8 − 3)! × 3!
✓
Topic check
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