in how many ways can 6 people apply for 2 different jobs?
The answer would depend of whether they can apply for both jobs
or whether they can only apply for 1 of the jobs.
I'll do it both ways.
Assuming they can do any of 3 things --
apply for either J only, K only, or both J and K
There are 3 things A can do, apply for J, K, or J&K
For each of the 3 things A can do, there are 3 things B can do.
That's 3×3=32=9 things A and B can do.
For each of the 3×3=32=9 things A and B can do, there
are 3 things C can do.
That's 3×3×3=33=27 things A,B, and C can do.
... etc. ...
For each of the 3×3×3×3×3=35=243 things A,B,C,D and E can do,
there are 3 things F can do.
That's 3×3×3×3×3×3=36=729 things A,B,C,D,E, and F can do.
Answer: 36=729
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Assuming they can only do either of 2 things --
apply for either J only or apply for K only.
[They can't apply for both jobs.]
There are 2 things A can do, apply to J or K
For each of the 2 things A can do, there are 2 things B can do.
That's 2×2=32=4 things A and B can do.
For each of the 2×2=22=4 things A and B can do, there
are 2 things C can do.
That's 2×2×2=23=8 things A,B, and C can do.
... etc. ...
For each of the 2×2×2×2×2=25=32 things A,B,C,D and E can do,
there are 2 things F can do.
That's 2×2×2×2×2×2=26=64 things A,B,C,D,E, and F can do.
Answer: 26=64
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Edwin
