Question

Kim wants to arrange chocolate, vanilla, and pineapple cakes in a row on a shelf. Which tree diagram best shows the sample space of all the possible ways to arrange the three cakes in a row on a shelf, where C is chocolate, V is vanilla, and P is pineapple?

A tree diagram is shown. The lines branch out to C, P, and V. In the first row, the lines branch out from C to V to C and from C to P to V. In the second row, the lines branch out from P to C to V and from P to V to P. In the last row, the lines branch out from V to C to P and from V to P to C.
A tree diagram is shown. The lines branch out to C, P, and V. In the first row, the lines branch out from C to V to P and from C to P to V. In the second row, the lines branch out from P to C to V and from P to V to C. In the last row, the lines branch out from V to C to P and from V to P to C.
A tree diagram is shown. The lines branch out to C, P, and V. In the first row, the lines branch out from C to V to P and from C to P to V. In the second row, the lines branch out from P to C to P and from P to V to C. In the last row, the lines branch out from V to C to V and from V to P to C.
A tree diagram is shown. The lines branch out to C, P, and V. In the first row, the lines branch out from C to V to P and from C to P to C. In the second row, the lines branch out from P to C to V and from P to V to C. In the last row, the lines branch out from V to C to P and from V to P to V.

Answer 1

yikes

anyway, let's start by sketching the first branch of the tree, which includes C, V, and P

Answer 2

there are only three cakes, so each branch can only contain C, P, and V once each

Answer 3

try to finish the tree and see which answer choice best represents what the tree looks like