# A golf club manufacturer makes drivers with 4 different shaft lengths, 3 different lofts, 2 different grips, and 2 different club head materials. How many different combinations are possible?

Oct 20, 2017

$48$ combinations

#### Explanation:

There is a formulaic way to solve this, but knowing the concept makes this problem understandable.

There are 4 different shafts: S1, S2, S3, and S4

And 3 different lofts: L1, L2, L3

Just looking at those combinations we have:

S1, L1
S2, L1
S3, L1
S4, L1
S1, L2
S2, L2
S3, L2
S4, L2
S1, L3
S2, L3
S3, L3
S4, L3

That is 12 combinations or $4 \cdot 3$

Then there are 2 different grips that all those combinations could have so that makes a total of $24$ combinations or $12 \cdot 2$

Then there are 2 different head materials that those $24$ combinations could have so that makes a total of $48$ or $24 \cdot 2$

Thus there are a total of $4 \cdot 3 \cdot 2 \cdot 2 = 48$ combinations