Question

Help please??
A delicatessen offers 4 different breads, 4 cheeses, and 6 different meats. In how many ways can a sandwich be made with 1 bread, 2 cheese and 3 meats?



360


420


480


540

Answer 1

Th required number of ways is given by:
\[4\times 4C2\times6C3=you\ can\ calculate\]

Answer 2

What do the C's stand for?

Answer 3

\[\large nCr=\frac{n!}{r!(n-r)!}\]
So 4C2 is
\[\large 4C2=\frac{4\times3\times2\times1}{2\times1\times2\times1}=6\]

Answer 4

And 6C3 is
\[\large 6C3=\frac{6\times5\times4\times3\times2\times1}{3\times2\times1\times3\times2\times1}=20\]

Answer 5

is it 480 then?

Answer 6

Correct.